A multi-point constraint unfitted finite element method

Abstract In this work a multi-point constraint unfitted finite element method for the solution of the Poisson equation is presented. Key features of the approach are the strong enforcement of essential boundary, and interface conditions. This, along with the stability of the method, is achieved thro...
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Autor*in:	Freeman, Brubeck Lee [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Unfitted finite element method Cut element stability Unfitted boundary conditions Multi-point constraints Unfitted interface Extra dof free

Anmerkung:	© The Author(s) 2022

Übergeordnetes Werk:	Enthalten in: Advanced modeling and simulation in engineering sciences - Berlin : SpringerOpen, 2014, 9(2022), 1 vom: 21. Sept.
Übergeordnetes Werk:	volume:9 ; year:2022 ; number:1 ; day:21 ; month:09

Links:	Volltext

DOI / URN:	10.1186/s40323-022-00232-w

Katalog-ID:	SPR048169226

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520			\|a Abstract In this work a multi-point constraint unfitted finite element method for the solution of the Poisson equation is presented. Key features of the approach are the strong enforcement of essential boundary, and interface conditions. This, along with the stability of the method, is achieved through the use of multi-point constraints that are applied to the so-called ghost nodes that lie outside of the physical domain. Another key benefit of the approach lies in the fact that, as the degrees of freedom associated with ghost nodes are constrained, they can be removed from the system of equations. This enables the method to capture both strong and weak discontinuities with no additional degrees of freedom. In addition, the method does not require penalty parameters and can capture discontinuities using only the standard finite element basis functions. Finally, numerical results show that the method converges optimally with mesh refinement and remains well conditioned.
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allfields	10.1186/s40323-022-00232-w doi (DE-627)SPR048169226 (SPR)s40323-022-00232-w-e DE-627 ger DE-627 rakwb eng Freeman, Brubeck Lee verfasserin (orcid)0000-0002-2414-5832 aut A multi-point constraint unfitted finite element method 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this work a multi-point constraint unfitted finite element method for the solution of the Poisson equation is presented. Key features of the approach are the strong enforcement of essential boundary, and interface conditions. This, along with the stability of the method, is achieved through the use of multi-point constraints that are applied to the so-called ghost nodes that lie outside of the physical domain. Another key benefit of the approach lies in the fact that, as the degrees of freedom associated with ghost nodes are constrained, they can be removed from the system of equations. This enables the method to capture both strong and weak discontinuities with no additional degrees of freedom. In addition, the method does not require penalty parameters and can capture discontinuities using only the standard finite element basis functions. Finally, numerical results show that the method converges optimally with mesh refinement and remains well conditioned. Unfitted finite element method (dpeaa)DE-He213 Cut element stability (dpeaa)DE-He213 Unfitted boundary conditions (dpeaa)DE-He213 Multi-point constraints (dpeaa)DE-He213 Unfitted interface (dpeaa)DE-He213 Extra dof free (dpeaa)DE-He213 Enthalten in Advanced modeling and simulation in engineering sciences Berlin : SpringerOpen, 2014 9(2022), 1 vom: 21. Sept. (DE-627)784191816 (DE-600)2767724-2 2213-7467 nnns volume:9 year:2022 number:1 day:21 month:09 https://dx.doi.org/10.1186/s40323-022-00232-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2022 1 21 09
spelling	10.1186/s40323-022-00232-w doi (DE-627)SPR048169226 (SPR)s40323-022-00232-w-e DE-627 ger DE-627 rakwb eng Freeman, Brubeck Lee verfasserin (orcid)0000-0002-2414-5832 aut A multi-point constraint unfitted finite element method 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this work a multi-point constraint unfitted finite element method for the solution of the Poisson equation is presented. Key features of the approach are the strong enforcement of essential boundary, and interface conditions. This, along with the stability of the method, is achieved through the use of multi-point constraints that are applied to the so-called ghost nodes that lie outside of the physical domain. Another key benefit of the approach lies in the fact that, as the degrees of freedom associated with ghost nodes are constrained, they can be removed from the system of equations. This enables the method to capture both strong and weak discontinuities with no additional degrees of freedom. In addition, the method does not require penalty parameters and can capture discontinuities using only the standard finite element basis functions. Finally, numerical results show that the method converges optimally with mesh refinement and remains well conditioned. Unfitted finite element method (dpeaa)DE-He213 Cut element stability (dpeaa)DE-He213 Unfitted boundary conditions (dpeaa)DE-He213 Multi-point constraints (dpeaa)DE-He213 Unfitted interface (dpeaa)DE-He213 Extra dof free (dpeaa)DE-He213 Enthalten in Advanced modeling and simulation in engineering sciences Berlin : SpringerOpen, 2014 9(2022), 1 vom: 21. Sept. (DE-627)784191816 (DE-600)2767724-2 2213-7467 nnns volume:9 year:2022 number:1 day:21 month:09 https://dx.doi.org/10.1186/s40323-022-00232-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2022 1 21 09
allfields_unstemmed	10.1186/s40323-022-00232-w doi (DE-627)SPR048169226 (SPR)s40323-022-00232-w-e DE-627 ger DE-627 rakwb eng Freeman, Brubeck Lee verfasserin (orcid)0000-0002-2414-5832 aut A multi-point constraint unfitted finite element method 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this work a multi-point constraint unfitted finite element method for the solution of the Poisson equation is presented. Key features of the approach are the strong enforcement of essential boundary, and interface conditions. This, along with the stability of the method, is achieved through the use of multi-point constraints that are applied to the so-called ghost nodes that lie outside of the physical domain. Another key benefit of the approach lies in the fact that, as the degrees of freedom associated with ghost nodes are constrained, they can be removed from the system of equations. This enables the method to capture both strong and weak discontinuities with no additional degrees of freedom. In addition, the method does not require penalty parameters and can capture discontinuities using only the standard finite element basis functions. Finally, numerical results show that the method converges optimally with mesh refinement and remains well conditioned. Unfitted finite element method (dpeaa)DE-He213 Cut element stability (dpeaa)DE-He213 Unfitted boundary conditions (dpeaa)DE-He213 Multi-point constraints (dpeaa)DE-He213 Unfitted interface (dpeaa)DE-He213 Extra dof free (dpeaa)DE-He213 Enthalten in Advanced modeling and simulation in engineering sciences Berlin : SpringerOpen, 2014 9(2022), 1 vom: 21. Sept. (DE-627)784191816 (DE-600)2767724-2 2213-7467 nnns volume:9 year:2022 number:1 day:21 month:09 https://dx.doi.org/10.1186/s40323-022-00232-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2022 1 21 09
allfieldsGer	10.1186/s40323-022-00232-w doi (DE-627)SPR048169226 (SPR)s40323-022-00232-w-e DE-627 ger DE-627 rakwb eng Freeman, Brubeck Lee verfasserin (orcid)0000-0002-2414-5832 aut A multi-point constraint unfitted finite element method 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this work a multi-point constraint unfitted finite element method for the solution of the Poisson equation is presented. Key features of the approach are the strong enforcement of essential boundary, and interface conditions. This, along with the stability of the method, is achieved through the use of multi-point constraints that are applied to the so-called ghost nodes that lie outside of the physical domain. Another key benefit of the approach lies in the fact that, as the degrees of freedom associated with ghost nodes are constrained, they can be removed from the system of equations. This enables the method to capture both strong and weak discontinuities with no additional degrees of freedom. In addition, the method does not require penalty parameters and can capture discontinuities using only the standard finite element basis functions. Finally, numerical results show that the method converges optimally with mesh refinement and remains well conditioned. Unfitted finite element method (dpeaa)DE-He213 Cut element stability (dpeaa)DE-He213 Unfitted boundary conditions (dpeaa)DE-He213 Multi-point constraints (dpeaa)DE-He213 Unfitted interface (dpeaa)DE-He213 Extra dof free (dpeaa)DE-He213 Enthalten in Advanced modeling and simulation in engineering sciences Berlin : SpringerOpen, 2014 9(2022), 1 vom: 21. Sept. (DE-627)784191816 (DE-600)2767724-2 2213-7467 nnns volume:9 year:2022 number:1 day:21 month:09 https://dx.doi.org/10.1186/s40323-022-00232-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2022 1 21 09
allfieldsSound	10.1186/s40323-022-00232-w doi (DE-627)SPR048169226 (SPR)s40323-022-00232-w-e DE-627 ger DE-627 rakwb eng Freeman, Brubeck Lee verfasserin (orcid)0000-0002-2414-5832 aut A multi-point constraint unfitted finite element method 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this work a multi-point constraint unfitted finite element method for the solution of the Poisson equation is presented. Key features of the approach are the strong enforcement of essential boundary, and interface conditions. This, along with the stability of the method, is achieved through the use of multi-point constraints that are applied to the so-called ghost nodes that lie outside of the physical domain. Another key benefit of the approach lies in the fact that, as the degrees of freedom associated with ghost nodes are constrained, they can be removed from the system of equations. This enables the method to capture both strong and weak discontinuities with no additional degrees of freedom. In addition, the method does not require penalty parameters and can capture discontinuities using only the standard finite element basis functions. Finally, numerical results show that the method converges optimally with mesh refinement and remains well conditioned. Unfitted finite element method (dpeaa)DE-He213 Cut element stability (dpeaa)DE-He213 Unfitted boundary conditions (dpeaa)DE-He213 Multi-point constraints (dpeaa)DE-He213 Unfitted interface (dpeaa)DE-He213 Extra dof free (dpeaa)DE-He213 Enthalten in Advanced modeling and simulation in engineering sciences Berlin : SpringerOpen, 2014 9(2022), 1 vom: 21. Sept. (DE-627)784191816 (DE-600)2767724-2 2213-7467 nnns volume:9 year:2022 number:1 day:21 month:09 https://dx.doi.org/10.1186/s40323-022-00232-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2022 1 21 09
language	English
source	Enthalten in Advanced modeling and simulation in engineering sciences 9(2022), 1 vom: 21. Sept. volume:9 year:2022 number:1 day:21 month:09
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topic_facet	Unfitted finite element method Cut element stability Unfitted boundary conditions Multi-point constraints Unfitted interface Extra dof free
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author	Freeman, Brubeck Lee
spellingShingle	Freeman, Brubeck Lee misc Unfitted finite element method misc Cut element stability misc Unfitted boundary conditions misc Multi-point constraints misc Unfitted interface misc Extra dof free A multi-point constraint unfitted finite element method
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topic_title	A multi-point constraint unfitted finite element method Unfitted finite element method (dpeaa)DE-He213 Cut element stability (dpeaa)DE-He213 Unfitted boundary conditions (dpeaa)DE-He213 Multi-point constraints (dpeaa)DE-He213 Unfitted interface (dpeaa)DE-He213 Extra dof free (dpeaa)DE-He213
topic	misc Unfitted finite element method misc Cut element stability misc Unfitted boundary conditions misc Multi-point constraints misc Unfitted interface misc Extra dof free
topic_unstemmed	misc Unfitted finite element method misc Cut element stability misc Unfitted boundary conditions misc Multi-point constraints misc Unfitted interface misc Extra dof free
topic_browse	misc Unfitted finite element method misc Cut element stability misc Unfitted boundary conditions misc Multi-point constraints misc Unfitted interface misc Extra dof free
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	A multi-point constraint unfitted finite element method
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title_full	A multi-point constraint unfitted finite element method
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title_sort	multi-point constraint unfitted finite element method
title_auth	A multi-point constraint unfitted finite element method
abstract	Abstract In this work a multi-point constraint unfitted finite element method for the solution of the Poisson equation is presented. Key features of the approach are the strong enforcement of essential boundary, and interface conditions. This, along with the stability of the method, is achieved through the use of multi-point constraints that are applied to the so-called ghost nodes that lie outside of the physical domain. Another key benefit of the approach lies in the fact that, as the degrees of freedom associated with ghost nodes are constrained, they can be removed from the system of equations. This enables the method to capture both strong and weak discontinuities with no additional degrees of freedom. In addition, the method does not require penalty parameters and can capture discontinuities using only the standard finite element basis functions. Finally, numerical results show that the method converges optimally with mesh refinement and remains well conditioned. © The Author(s) 2022
abstractGer	Abstract In this work a multi-point constraint unfitted finite element method for the solution of the Poisson equation is presented. Key features of the approach are the strong enforcement of essential boundary, and interface conditions. This, along with the stability of the method, is achieved through the use of multi-point constraints that are applied to the so-called ghost nodes that lie outside of the physical domain. Another key benefit of the approach lies in the fact that, as the degrees of freedom associated with ghost nodes are constrained, they can be removed from the system of equations. This enables the method to capture both strong and weak discontinuities with no additional degrees of freedom. In addition, the method does not require penalty parameters and can capture discontinuities using only the standard finite element basis functions. Finally, numerical results show that the method converges optimally with mesh refinement and remains well conditioned. © The Author(s) 2022
abstract_unstemmed	Abstract In this work a multi-point constraint unfitted finite element method for the solution of the Poisson equation is presented. Key features of the approach are the strong enforcement of essential boundary, and interface conditions. This, along with the stability of the method, is achieved through the use of multi-point constraints that are applied to the so-called ghost nodes that lie outside of the physical domain. Another key benefit of the approach lies in the fact that, as the degrees of freedom associated with ghost nodes are constrained, they can be removed from the system of equations. This enables the method to capture both strong and weak discontinuities with no additional degrees of freedom. In addition, the method does not require penalty parameters and can capture discontinuities using only the standard finite element basis functions. Finally, numerical results show that the method converges optimally with mesh refinement and remains well conditioned. © The Author(s) 2022
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title_short	A multi-point constraint unfitted finite element method
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