A comparison of dual Lagrange multiplier spaces for Mortar finite element discretizations

Barbara I. Wohlmuth

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2002)

  • Volume: 36, Issue: 6, page 995-1012
  • ISSN: 0764-583X

Abstract

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Domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We focus on mortar finite element methods on non-matching triangulations. In particular, we discuss and analyze dual Lagrange multiplier spaces for lowest order finite elements. These non standard Lagrange multiplier spaces yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces. As a consequence, standard efficient iterative solvers as multigrid methods or domain decomposition techniques can be easily adapted to the nonconforming situation. Here, we introduce new dual Lagrange multiplier spaces. We concentrate on the construction of locally supported and continuous dual basis functions. The optimality of the associated mortar method is shown. Numerical results illustrate the performance of our approach.

How to cite

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Wohlmuth, Barbara I.. "A comparison of dual Lagrange multiplier spaces for Mortar finite element discretizations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.6 (2002): 995-1012. <http://eudml.org/doc/244915>.

@article{Wohlmuth2002,
abstract = {Domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We focus on mortar finite element methods on non-matching triangulations. In particular, we discuss and analyze dual Lagrange multiplier spaces for lowest order finite elements. These non standard Lagrange multiplier spaces yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces. As a consequence, standard efficient iterative solvers as multigrid methods or domain decomposition techniques can be easily adapted to the nonconforming situation. Here, we introduce new dual Lagrange multiplier spaces. We concentrate on the construction of locally supported and continuous dual basis functions. The optimality of the associated mortar method is shown. Numerical results illustrate the performance of our approach.},
author = {Wohlmuth, Barbara I.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Mortar finite elements; dual space; non-matching triangulations; multigrid methods; mortar finite elements; second-order elliptic boundary value problem; domain decomposition; dual Lagrange multiplier spaces; numerical results},
language = {eng},
number = {6},
pages = {995-1012},
publisher = {EDP-Sciences},
title = {A comparison of dual Lagrange multiplier spaces for Mortar finite element discretizations},
url = {http://eudml.org/doc/244915},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Wohlmuth, Barbara I.
TI - A comparison of dual Lagrange multiplier spaces for Mortar finite element discretizations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 6
SP - 995
EP - 1012
AB - Domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We focus on mortar finite element methods on non-matching triangulations. In particular, we discuss and analyze dual Lagrange multiplier spaces for lowest order finite elements. These non standard Lagrange multiplier spaces yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces. As a consequence, standard efficient iterative solvers as multigrid methods or domain decomposition techniques can be easily adapted to the nonconforming situation. Here, we introduce new dual Lagrange multiplier spaces. We concentrate on the construction of locally supported and continuous dual basis functions. The optimality of the associated mortar method is shown. Numerical results illustrate the performance of our approach.
LA - eng
KW - Mortar finite elements; dual space; non-matching triangulations; multigrid methods; mortar finite elements; second-order elliptic boundary value problem; domain decomposition; dual Lagrange multiplier spaces; numerical results
UR - http://eudml.org/doc/244915
ER -

References

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  11. [11] P. Oswald and B. Wohlmuth, On polynomial reproduction of dual FE bases, in: Thirteenth Int. Conf. on Domain Decomposition Methods (2002) 85–96. Zbl1026.65098
  12. [12] B.I. Wohlmuth and R.H. Krause, Multigrid methods based on the unconstrained product space arising from mortar finite element discretizations. SIAM J. Numer. Anal. 39 (2001) 192–213. Zbl0992.65142
  13. [13] B.I. Wohlmuth, A mortar finite element method using dual spaces for the Lagrange multiplier. SIAM J. Numer. Anal. 38 (2000) 989–1012. Zbl0974.65105
  14. [14] B.I. Wohlmuth, Discretization methods and iterative solvers based on domain decomposition. Lecture Notes in Comput. Sci. 17, Springer, Heidelberg (2001). Zbl0966.65097MR1820470

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