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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.
@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: Mathematical Modelling and Numerical Analysis },
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://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis PY - 2004 SP - 73 EP - 92 VL - 38 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis %D 2004 %P 73-92 %V 38 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 1, pp. 73-92. doi: 10.1051/m2an:2004004
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