A Comparison of Dual Lagrange Multiplier Spaces for Mortar Finite Element Discretizations

Barbara I. Wohlmuth

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • 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 36.6 (2010): 995-1012. <http://eudml.org/doc/194147>.

@article{Wohlmuth2010,
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},
keywords = {Mortar finite elements; dual space; non-matching triangulations; multigrid methods.; mortar finite elements; second-order elliptic boundary value problem; non-matching triangulations; multigrid methods; domain decomposition; dual Lagrange multiplier spaces; numerical results},
language = {eng},
month = {3},
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/194147},
volume = {36},
year = {2010},
}

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
DA - 2010/3//
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; non-matching triangulations; multigrid methods; domain decomposition; dual Lagrange multiplier spaces; numerical results
UR - http://eudml.org/doc/194147
ER -

References

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  9. R.H. Krause and B.I. Wohlmuth, Nonconforming domain decomposition techniques for linear elasticity. East-West J. Numer. Math.8 (2000) 177-206.  
  10. Y. Maday, F. Rapetti and B.I. Wohlmuth, The influence of quadrature formulas in 3d mortar methods. Lect. Notes Comput. Sci. Eng. 22, Springer-Verlag (2002).  
  11. P. Oswald and B. Wohlmuth, On polynomial reproduction of dual FE bases, in: Thirteenth Int. Conf. on Domain Decomposition Methods (2002) 85-96.  
  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.  
  13. B.I. Wohlmuth, A mortar finite element method using dual spaces for the Lagrange multiplier. SIAM J. Numer. Anal.38 (2000) 989-1012.  
  14. B.I. Wohlmuth, Discretization methods and iterative solvers based on domain decomposition. Lecture Notes in Comput. Sci. 17, Springer, Heidelberg (2001).  

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