Analysis and computation of continuous data assimilation algorithms for Lorenz 63 system based on nonlinear nudging techniques
In this work, continuous data assimilation algorithms based on three nonlinear nudging techniques (simple power nonlinearity, hybrid linear–nonlinear method and concave–convex nonlinearity) are studied for Lorenz 63 system to speed up the convergence rate of the approximate solution to the reference...
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| Autor*in: |
Du, Yi Juan [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021transfer abstract |
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| Übergeordnetes Werk: |
Enthalten in: Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics - Hu, Xing ELSEVIER, 2015transfer abstract, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:386 ; year:2021 ; pages:0 |
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| DOI / URN: |
10.1016/j.cam.2020.113246 |
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| 520 | |a In this work, continuous data assimilation algorithms based on three nonlinear nudging techniques (simple power nonlinearity, hybrid linear–nonlinear method and concave–convex nonlinearity) are studied for Lorenz 63 system to speed up the convergence rate of the approximate solution to the reference solution. The well-posedness of these three nonlinear continuous data assimilation algorithms are proven. For two cases that include synchronizing the first or second variable only are considered, the approximate solution is proven to converge to the reference solution as times go to infinity provided that the relaxed parameter related to the corresponding variable is sufficiently large. The byproduct of the proof is to observe that for these three nonlinear nudging techniques, synchronizing the second variable could be more efficient than synchronizing the first variable because the convergence rate for the first variable is shown to be slower than the second variable. Although the convergence rate may not be optimal, this still gives some possible explanation why synchronizing the second variable is more efficient than synchronizing the first which are numerically found in our numerical simulations. Moreover, numerical simulations are presented to illustrate the advantages of continuous data assimilation algorithms based on nonlinear nudging techniques. Some open problems arising from numerical experiments are reported. | ||
| 520 | |a In this work, continuous data assimilation algorithms based on three nonlinear nudging techniques (simple power nonlinearity, hybrid linear–nonlinear method and concave–convex nonlinearity) are studied for Lorenz 63 system to speed up the convergence rate of the approximate solution to the reference solution. The well-posedness of these three nonlinear continuous data assimilation algorithms are proven. For two cases that include synchronizing the first or second variable only are considered, the approximate solution is proven to converge to the reference solution as times go to infinity provided that the relaxed parameter related to the corresponding variable is sufficiently large. The byproduct of the proof is to observe that for these three nonlinear nudging techniques, synchronizing the second variable could be more efficient than synchronizing the first variable because the convergence rate for the first variable is shown to be slower than the second variable. Although the convergence rate may not be optimal, this still gives some possible explanation why synchronizing the second variable is more efficient than synchronizing the first which are numerically found in our numerical simulations. Moreover, numerical simulations are presented to illustrate the advantages of continuous data assimilation algorithms based on nonlinear nudging techniques. Some open problems arising from numerical experiments are reported. | ||
| 650 | 7 | |a Lorenz 63 system |2 Elsevier | |
| 650 | 7 | |a Nonlinear nudging techniques |2 Elsevier | |
| 650 | 7 | |a Speed up |2 Elsevier | |
| 650 | 7 | |a Continuous data assimilation algorithms |2 Elsevier | |
| 650 | 7 | |a Synchronization |2 Elsevier | |
| 650 | 7 | |a Convergence |2 Elsevier | |
| 700 | 1 | |a Shiue, Ming-Cheng |4 oth | |
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10.1016/j.cam.2020.113246 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001222.pica (DE-627)ELV052266044 (ELSEVIER)S0377-0427(20)30537-9 DE-627 ger DE-627 rakwb eng 670 VZ 540 VZ 630 VZ Du, Yi Juan verfasserin aut Analysis and computation of continuous data assimilation algorithms for Lorenz 63 system based on nonlinear nudging techniques 2021transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this work, continuous data assimilation algorithms based on three nonlinear nudging techniques (simple power nonlinearity, hybrid linear–nonlinear method and concave–convex nonlinearity) are studied for Lorenz 63 system to speed up the convergence rate of the approximate solution to the reference solution. The well-posedness of these three nonlinear continuous data assimilation algorithms are proven. For two cases that include synchronizing the first or second variable only are considered, the approximate solution is proven to converge to the reference solution as times go to infinity provided that the relaxed parameter related to the corresponding variable is sufficiently large. The byproduct of the proof is to observe that for these three nonlinear nudging techniques, synchronizing the second variable could be more efficient than synchronizing the first variable because the convergence rate for the first variable is shown to be slower than the second variable. Although the convergence rate may not be optimal, this still gives some possible explanation why synchronizing the second variable is more efficient than synchronizing the first which are numerically found in our numerical simulations. Moreover, numerical simulations are presented to illustrate the advantages of continuous data assimilation algorithms based on nonlinear nudging techniques. Some open problems arising from numerical experiments are reported. In this work, continuous data assimilation algorithms based on three nonlinear nudging techniques (simple power nonlinearity, hybrid linear–nonlinear method and concave–convex nonlinearity) are studied for Lorenz 63 system to speed up the convergence rate of the approximate solution to the reference solution. The well-posedness of these three nonlinear continuous data assimilation algorithms are proven. For two cases that include synchronizing the first or second variable only are considered, the approximate solution is proven to converge to the reference solution as times go to infinity provided that the relaxed parameter related to the corresponding variable is sufficiently large. The byproduct of the proof is to observe that for these three nonlinear nudging techniques, synchronizing the second variable could be more efficient than synchronizing the first variable because the convergence rate for the first variable is shown to be slower than the second variable. Although the convergence rate may not be optimal, this still gives some possible explanation why synchronizing the second variable is more efficient than synchronizing the first which are numerically found in our numerical simulations. Moreover, numerical simulations are presented to illustrate the advantages of continuous data assimilation algorithms based on nonlinear nudging techniques. Some open problems arising from numerical experiments are reported. Lorenz 63 system Elsevier Nonlinear nudging techniques Elsevier Speed up Elsevier Continuous data assimilation algorithms Elsevier Synchronization Elsevier Convergence Elsevier Shiue, Ming-Cheng oth Enthalten in North-Holland Hu, Xing ELSEVIER Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV013217658 volume:386 year:2021 pages:0 https://doi.org/10.1016/j.cam.2020.113246 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 386 2021 0 |
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10.1016/j.cam.2020.113246 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001222.pica (DE-627)ELV052266044 (ELSEVIER)S0377-0427(20)30537-9 DE-627 ger DE-627 rakwb eng 670 VZ 540 VZ 630 VZ Du, Yi Juan verfasserin aut Analysis and computation of continuous data assimilation algorithms for Lorenz 63 system based on nonlinear nudging techniques 2021transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this work, continuous data assimilation algorithms based on three nonlinear nudging techniques (simple power nonlinearity, hybrid linear–nonlinear method and concave–convex nonlinearity) are studied for Lorenz 63 system to speed up the convergence rate of the approximate solution to the reference solution. The well-posedness of these three nonlinear continuous data assimilation algorithms are proven. For two cases that include synchronizing the first or second variable only are considered, the approximate solution is proven to converge to the reference solution as times go to infinity provided that the relaxed parameter related to the corresponding variable is sufficiently large. The byproduct of the proof is to observe that for these three nonlinear nudging techniques, synchronizing the second variable could be more efficient than synchronizing the first variable because the convergence rate for the first variable is shown to be slower than the second variable. Although the convergence rate may not be optimal, this still gives some possible explanation why synchronizing the second variable is more efficient than synchronizing the first which are numerically found in our numerical simulations. Moreover, numerical simulations are presented to illustrate the advantages of continuous data assimilation algorithms based on nonlinear nudging techniques. Some open problems arising from numerical experiments are reported. In this work, continuous data assimilation algorithms based on three nonlinear nudging techniques (simple power nonlinearity, hybrid linear–nonlinear method and concave–convex nonlinearity) are studied for Lorenz 63 system to speed up the convergence rate of the approximate solution to the reference solution. The well-posedness of these three nonlinear continuous data assimilation algorithms are proven. For two cases that include synchronizing the first or second variable only are considered, the approximate solution is proven to converge to the reference solution as times go to infinity provided that the relaxed parameter related to the corresponding variable is sufficiently large. The byproduct of the proof is to observe that for these three nonlinear nudging techniques, synchronizing the second variable could be more efficient than synchronizing the first variable because the convergence rate for the first variable is shown to be slower than the second variable. Although the convergence rate may not be optimal, this still gives some possible explanation why synchronizing the second variable is more efficient than synchronizing the first which are numerically found in our numerical simulations. Moreover, numerical simulations are presented to illustrate the advantages of continuous data assimilation algorithms based on nonlinear nudging techniques. Some open problems arising from numerical experiments are reported. Lorenz 63 system Elsevier Nonlinear nudging techniques Elsevier Speed up Elsevier Continuous data assimilation algorithms Elsevier Synchronization Elsevier Convergence Elsevier Shiue, Ming-Cheng oth Enthalten in North-Holland Hu, Xing ELSEVIER Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV013217658 volume:386 year:2021 pages:0 https://doi.org/10.1016/j.cam.2020.113246 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 386 2021 0 |
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10.1016/j.cam.2020.113246 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001222.pica (DE-627)ELV052266044 (ELSEVIER)S0377-0427(20)30537-9 DE-627 ger DE-627 rakwb eng 670 VZ 540 VZ 630 VZ Du, Yi Juan verfasserin aut Analysis and computation of continuous data assimilation algorithms for Lorenz 63 system based on nonlinear nudging techniques 2021transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this work, continuous data assimilation algorithms based on three nonlinear nudging techniques (simple power nonlinearity, hybrid linear–nonlinear method and concave–convex nonlinearity) are studied for Lorenz 63 system to speed up the convergence rate of the approximate solution to the reference solution. The well-posedness of these three nonlinear continuous data assimilation algorithms are proven. For two cases that include synchronizing the first or second variable only are considered, the approximate solution is proven to converge to the reference solution as times go to infinity provided that the relaxed parameter related to the corresponding variable is sufficiently large. The byproduct of the proof is to observe that for these three nonlinear nudging techniques, synchronizing the second variable could be more efficient than synchronizing the first variable because the convergence rate for the first variable is shown to be slower than the second variable. Although the convergence rate may not be optimal, this still gives some possible explanation why synchronizing the second variable is more efficient than synchronizing the first which are numerically found in our numerical simulations. Moreover, numerical simulations are presented to illustrate the advantages of continuous data assimilation algorithms based on nonlinear nudging techniques. Some open problems arising from numerical experiments are reported. In this work, continuous data assimilation algorithms based on three nonlinear nudging techniques (simple power nonlinearity, hybrid linear–nonlinear method and concave–convex nonlinearity) are studied for Lorenz 63 system to speed up the convergence rate of the approximate solution to the reference solution. The well-posedness of these three nonlinear continuous data assimilation algorithms are proven. For two cases that include synchronizing the first or second variable only are considered, the approximate solution is proven to converge to the reference solution as times go to infinity provided that the relaxed parameter related to the corresponding variable is sufficiently large. The byproduct of the proof is to observe that for these three nonlinear nudging techniques, synchronizing the second variable could be more efficient than synchronizing the first variable because the convergence rate for the first variable is shown to be slower than the second variable. Although the convergence rate may not be optimal, this still gives some possible explanation why synchronizing the second variable is more efficient than synchronizing the first which are numerically found in our numerical simulations. Moreover, numerical simulations are presented to illustrate the advantages of continuous data assimilation algorithms based on nonlinear nudging techniques. Some open problems arising from numerical experiments are reported. Lorenz 63 system Elsevier Nonlinear nudging techniques Elsevier Speed up Elsevier Continuous data assimilation algorithms Elsevier Synchronization Elsevier Convergence Elsevier Shiue, Ming-Cheng oth Enthalten in North-Holland Hu, Xing ELSEVIER Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV013217658 volume:386 year:2021 pages:0 https://doi.org/10.1016/j.cam.2020.113246 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 386 2021 0 |
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10.1016/j.cam.2020.113246 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001222.pica (DE-627)ELV052266044 (ELSEVIER)S0377-0427(20)30537-9 DE-627 ger DE-627 rakwb eng 670 VZ 540 VZ 630 VZ Du, Yi Juan verfasserin aut Analysis and computation of continuous data assimilation algorithms for Lorenz 63 system based on nonlinear nudging techniques 2021transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this work, continuous data assimilation algorithms based on three nonlinear nudging techniques (simple power nonlinearity, hybrid linear–nonlinear method and concave–convex nonlinearity) are studied for Lorenz 63 system to speed up the convergence rate of the approximate solution to the reference solution. The well-posedness of these three nonlinear continuous data assimilation algorithms are proven. For two cases that include synchronizing the first or second variable only are considered, the approximate solution is proven to converge to the reference solution as times go to infinity provided that the relaxed parameter related to the corresponding variable is sufficiently large. The byproduct of the proof is to observe that for these three nonlinear nudging techniques, synchronizing the second variable could be more efficient than synchronizing the first variable because the convergence rate for the first variable is shown to be slower than the second variable. Although the convergence rate may not be optimal, this still gives some possible explanation why synchronizing the second variable is more efficient than synchronizing the first which are numerically found in our numerical simulations. Moreover, numerical simulations are presented to illustrate the advantages of continuous data assimilation algorithms based on nonlinear nudging techniques. Some open problems arising from numerical experiments are reported. In this work, continuous data assimilation algorithms based on three nonlinear nudging techniques (simple power nonlinearity, hybrid linear–nonlinear method and concave–convex nonlinearity) are studied for Lorenz 63 system to speed up the convergence rate of the approximate solution to the reference solution. The well-posedness of these three nonlinear continuous data assimilation algorithms are proven. For two cases that include synchronizing the first or second variable only are considered, the approximate solution is proven to converge to the reference solution as times go to infinity provided that the relaxed parameter related to the corresponding variable is sufficiently large. The byproduct of the proof is to observe that for these three nonlinear nudging techniques, synchronizing the second variable could be more efficient than synchronizing the first variable because the convergence rate for the first variable is shown to be slower than the second variable. Although the convergence rate may not be optimal, this still gives some possible explanation why synchronizing the second variable is more efficient than synchronizing the first which are numerically found in our numerical simulations. Moreover, numerical simulations are presented to illustrate the advantages of continuous data assimilation algorithms based on nonlinear nudging techniques. Some open problems arising from numerical experiments are reported. Lorenz 63 system Elsevier Nonlinear nudging techniques Elsevier Speed up Elsevier Continuous data assimilation algorithms Elsevier Synchronization Elsevier Convergence Elsevier Shiue, Ming-Cheng oth Enthalten in North-Holland Hu, Xing ELSEVIER Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV013217658 volume:386 year:2021 pages:0 https://doi.org/10.1016/j.cam.2020.113246 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 386 2021 0 |
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10.1016/j.cam.2020.113246 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001222.pica (DE-627)ELV052266044 (ELSEVIER)S0377-0427(20)30537-9 DE-627 ger DE-627 rakwb eng 670 VZ 540 VZ 630 VZ Du, Yi Juan verfasserin aut Analysis and computation of continuous data assimilation algorithms for Lorenz 63 system based on nonlinear nudging techniques 2021transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this work, continuous data assimilation algorithms based on three nonlinear nudging techniques (simple power nonlinearity, hybrid linear–nonlinear method and concave–convex nonlinearity) are studied for Lorenz 63 system to speed up the convergence rate of the approximate solution to the reference solution. The well-posedness of these three nonlinear continuous data assimilation algorithms are proven. For two cases that include synchronizing the first or second variable only are considered, the approximate solution is proven to converge to the reference solution as times go to infinity provided that the relaxed parameter related to the corresponding variable is sufficiently large. The byproduct of the proof is to observe that for these three nonlinear nudging techniques, synchronizing the second variable could be more efficient than synchronizing the first variable because the convergence rate for the first variable is shown to be slower than the second variable. Although the convergence rate may not be optimal, this still gives some possible explanation why synchronizing the second variable is more efficient than synchronizing the first which are numerically found in our numerical simulations. Moreover, numerical simulations are presented to illustrate the advantages of continuous data assimilation algorithms based on nonlinear nudging techniques. Some open problems arising from numerical experiments are reported. In this work, continuous data assimilation algorithms based on three nonlinear nudging techniques (simple power nonlinearity, hybrid linear–nonlinear method and concave–convex nonlinearity) are studied for Lorenz 63 system to speed up the convergence rate of the approximate solution to the reference solution. The well-posedness of these three nonlinear continuous data assimilation algorithms are proven. For two cases that include synchronizing the first or second variable only are considered, the approximate solution is proven to converge to the reference solution as times go to infinity provided that the relaxed parameter related to the corresponding variable is sufficiently large. The byproduct of the proof is to observe that for these three nonlinear nudging techniques, synchronizing the second variable could be more efficient than synchronizing the first variable because the convergence rate for the first variable is shown to be slower than the second variable. Although the convergence rate may not be optimal, this still gives some possible explanation why synchronizing the second variable is more efficient than synchronizing the first which are numerically found in our numerical simulations. Moreover, numerical simulations are presented to illustrate the advantages of continuous data assimilation algorithms based on nonlinear nudging techniques. Some open problems arising from numerical experiments are reported. Lorenz 63 system Elsevier Nonlinear nudging techniques Elsevier Speed up Elsevier Continuous data assimilation algorithms Elsevier Synchronization Elsevier Convergence Elsevier Shiue, Ming-Cheng oth Enthalten in North-Holland Hu, Xing ELSEVIER Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV013217658 volume:386 year:2021 pages:0 https://doi.org/10.1016/j.cam.2020.113246 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 386 2021 0 |
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Enthalten in Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics Amsterdam [u.a.] volume:386 year:2021 pages:0 |
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Enthalten in Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics Amsterdam [u.a.] volume:386 year:2021 pages:0 |
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Lorenz 63 system Nonlinear nudging techniques Speed up Continuous data assimilation algorithms Synchronization Convergence |
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Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics |
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analysis and computation of continuous data assimilation algorithms for lorenz 63 system based on nonlinear nudging techniques |
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Analysis and computation of continuous data assimilation algorithms for Lorenz 63 system based on nonlinear nudging techniques |
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In this work, continuous data assimilation algorithms based on three nonlinear nudging techniques (simple power nonlinearity, hybrid linear–nonlinear method and concave–convex nonlinearity) are studied for Lorenz 63 system to speed up the convergence rate of the approximate solution to the reference solution. The well-posedness of these three nonlinear continuous data assimilation algorithms are proven. For two cases that include synchronizing the first or second variable only are considered, the approximate solution is proven to converge to the reference solution as times go to infinity provided that the relaxed parameter related to the corresponding variable is sufficiently large. The byproduct of the proof is to observe that for these three nonlinear nudging techniques, synchronizing the second variable could be more efficient than synchronizing the first variable because the convergence rate for the first variable is shown to be slower than the second variable. Although the convergence rate may not be optimal, this still gives some possible explanation why synchronizing the second variable is more efficient than synchronizing the first which are numerically found in our numerical simulations. Moreover, numerical simulations are presented to illustrate the advantages of continuous data assimilation algorithms based on nonlinear nudging techniques. Some open problems arising from numerical experiments are reported. |
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In this work, continuous data assimilation algorithms based on three nonlinear nudging techniques (simple power nonlinearity, hybrid linear–nonlinear method and concave–convex nonlinearity) are studied for Lorenz 63 system to speed up the convergence rate of the approximate solution to the reference solution. The well-posedness of these three nonlinear continuous data assimilation algorithms are proven. For two cases that include synchronizing the first or second variable only are considered, the approximate solution is proven to converge to the reference solution as times go to infinity provided that the relaxed parameter related to the corresponding variable is sufficiently large. The byproduct of the proof is to observe that for these three nonlinear nudging techniques, synchronizing the second variable could be more efficient than synchronizing the first variable because the convergence rate for the first variable is shown to be slower than the second variable. Although the convergence rate may not be optimal, this still gives some possible explanation why synchronizing the second variable is more efficient than synchronizing the first which are numerically found in our numerical simulations. Moreover, numerical simulations are presented to illustrate the advantages of continuous data assimilation algorithms based on nonlinear nudging techniques. Some open problems arising from numerical experiments are reported. |
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In this work, continuous data assimilation algorithms based on three nonlinear nudging techniques (simple power nonlinearity, hybrid linear–nonlinear method and concave–convex nonlinearity) are studied for Lorenz 63 system to speed up the convergence rate of the approximate solution to the reference solution. The well-posedness of these three nonlinear continuous data assimilation algorithms are proven. For two cases that include synchronizing the first or second variable only are considered, the approximate solution is proven to converge to the reference solution as times go to infinity provided that the relaxed parameter related to the corresponding variable is sufficiently large. The byproduct of the proof is to observe that for these three nonlinear nudging techniques, synchronizing the second variable could be more efficient than synchronizing the first variable because the convergence rate for the first variable is shown to be slower than the second variable. Although the convergence rate may not be optimal, this still gives some possible explanation why synchronizing the second variable is more efficient than synchronizing the first which are numerically found in our numerical simulations. Moreover, numerical simulations are presented to illustrate the advantages of continuous data assimilation algorithms based on nonlinear nudging techniques. Some open problems arising from numerical experiments are reported. |
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