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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.
@article{M2AN_2002__36_6_995_0,
author = {Wohlmuth, Barbara I.},
title = {A comparison of dual {Lagrange} multiplier spaces for {Mortar} finite element discretizations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {995--1012},
publisher = {EDP-Sciences},
volume = {36},
number = {6},
year = {2002},
doi = {10.1051/m2an:2003002},
mrnumber = {1958655},
zbl = {1024.65111},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2003002/}
}
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 PY - 2002 SP - 995 EP - 1012 VL - 36 IS - 6 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2003002/ DO - 10.1051/m2an:2003002 LA - en ID - M2AN_2002__36_6_995_0 ER -
%0 Journal Article %A Wohlmuth, Barbara I. %T A comparison of dual Lagrange multiplier spaces for Mortar finite element discretizations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2002 %P 995-1012 %V 36 %N 6 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2003002/ %R 10.1051/m2an:2003002 %G en %F M2AN_2002__36_6_995_0
Wohlmuth, Barbara I. A comparison of dual Lagrange multiplier spaces for Mortar finite element discretizations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 36 (2002) no. 6, pp. 995-1012. doi: 10.1051/m2an:2003002
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