Finite element methods on non-conforming grids by penalizing the matching constraint

Eric Boillat

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 2, page 357-372
  • ISSN: 0764-583X

Abstract

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The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.

How to cite

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Boillat, Eric. "Finite element methods on non-conforming grids by penalizing the matching constraint." ESAIM: Mathematical Modelling and Numerical Analysis 37.2 (2010): 357-372. <http://eudml.org/doc/194168>.

@article{Boillat2010,
abstract = { The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence. },
author = {Boillat, Eric},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Finite element methods; non-matching grids; penalty technique.; elliptic problems; error estimate; finite element methods; penalty technique},
language = {eng},
month = {3},
number = {2},
pages = {357-372},
publisher = {EDP Sciences},
title = {Finite element methods on non-conforming grids by penalizing the matching constraint},
url = {http://eudml.org/doc/194168},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Boillat, Eric
TI - Finite element methods on non-conforming grids by penalizing the matching constraint
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 2
SP - 357
EP - 372
AB - The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.
LA - eng
KW - Finite element methods; non-matching grids; penalty technique.; elliptic problems; error estimate; finite element methods; penalty technique
UR - http://eudml.org/doc/194168
ER -

References

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  10. Y. Maday, C. Bernardi and A.T. Patera, A new nonconforming approach to domain decomposition: the mortar element method, in Nonlinear Partial Differential Equations and their applications, H. Brezis and J.L. Lions Eds., Vol. XI, Pitman (1994) 13-51.  
  11. J. Nitsche, Über eine Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg 36 (1970/1971) 9-15.  
  12. D. Schotzau, C. Schwab and R. Stenberg, Mixed hp-fem on anisotropic meshes ii. Hanging nodes and tensor products of boundary layer meshes. Numer. Math.83 (1999) 667-697.  
  13. R. Stenberg, On some techniques for approximating boundary conditions in the finite element method. J. Comput. Appl. Math.63 (1995) 139-148.  

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