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

Eric Boillat

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2003)

  • 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 - Modélisation Mathématique et Analyse Numérique 37.2 (2003): 357-372. <http://eudml.org/doc/244673>.

@article{Boillat2003,
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 - Modélisation Mathématique et Analyse Numérique},
keywords = {finite element methods; non-matching grids; penalty technique; elliptic problems; error estimate},
language = {eng},
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/244673},
volume = {37},
year = {2003},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2003
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
UR - http://eudml.org/doc/244673
ER -

References

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  10. [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. Zbl0797.65094
  11. [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. Zbl0229.65079
  12. [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. Zbl0958.76049
  13. [13] R. Stenberg, On some techniques for approximating boundary conditions in the finite element method. J. Comput. Appl. Math. 63 (1995) 139–148. Zbl0856.65130

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