Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces in case of hexahedral triangulations. As a result, standard efficient iterative solvers as multigrid methods can be easily adapted to the nonconforming situation. We present the discretization errors in different norms for linear and quadratic mortar finite elements with different Lagrange multiplier spaces. Numerical results illustrate the performance of our approach.
Mots-clés : Mortar finite elements, Lagrange multiplier, dual space, domain decomposition, nonmatching triangulation
@article{M2AN_2004__38_1_73_0,
author = {Lamichhane, Bishnu P. and Wohlmuth, Barbara I.},
title = {A quasi-dual {Lagrange} multiplier space for serendipity mortar finite elements in {3D}},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {73--92},
publisher = {EDP-Sciences},
volume = {38},
number = {1},
year = {2004},
doi = {10.1051/m2an:2004004},
mrnumber = {2073931},
zbl = {1105.65352},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2004004/}
}
TY - JOUR AU - Lamichhane, Bishnu P. AU - Wohlmuth, Barbara I. TI - A quasi-dual Lagrange multiplier space for serendipity mortar finite elements in 3D JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 73 EP - 92 VL - 38 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2004004/ DO - 10.1051/m2an:2004004 LA - en ID - M2AN_2004__38_1_73_0 ER -
%0 Journal Article %A Lamichhane, Bishnu P. %A Wohlmuth, Barbara I. %T A quasi-dual Lagrange multiplier space for serendipity mortar finite elements in 3D %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 73-92 %V 38 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2004004/ %R 10.1051/m2an:2004004 %G en %F M2AN_2004__38_1_73_0
Lamichhane, Bishnu P.; Wohlmuth, Barbara I. A quasi-dual Lagrange multiplier space for serendipity mortar finite elements in 3D. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 1, pp. 73-92. doi : 10.1051/m2an:2004004. http://archive.numdam.org/articles/10.1051/m2an:2004004/
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