A quasi-dual Lagrange multiplier space for serendipity mortar finite elements in 3D
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 1, p. 73-92

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.

DOI : https://doi.org/10.1051/m2an:2004004
Classification:  35N55,  65N30
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {1},
     year = {2004},
     pages = {73-92},
     doi = {10.1051/m2an:2004004},
     zbl = {1105.65352},
     mrnumber = {2073931},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 1, pp. 73-92. doi : 10.1051/m2an:2004004. http://www.numdam.org/item/M2AN_2004__38_1_73_0/

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