We build and analyze a substructuring preconditioner for the Mortar method, applied to elliptic problems, in the - finite element framework. Particular attention is given to the construction of the coarse component of the preconditioner in this framework, in which continuity at the cross points is not required. Two variants are proposed: the first one is an improved version of a coarse preconditioner already presented in [S. Bertoluzza and M. Pennacchio, Appl. Numer. Anal. Comput. Math. 1 (2004) 434–454]. The second is new and is built by using a Discontinuous Galerkin interior penalty method as coarse problem. A bound of the condition number is proven for both variants and their efficiency and scalability is illustrated by numerical experiments.
Mots-clés : Domain decomposition methods, iterative substructuring, mortar method, h-pFEM
@article{M2AN_2016__50_4_1057_0,
author = {Bertoluzza, Silvia and Pennacchio, Micol and Prud{\textquoteright}homme, Christophe and Samake, Abdoulaye},
title = {Substructuring preconditioners for $h - p$ {Mortar} {FEM}},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1057--1082},
publisher = {EDP-Sciences},
volume = {50},
number = {4},
year = {2016},
doi = {10.1051/m2an/2015065},
zbl = {1350.65116},
mrnumber = {3521712},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2015065/}
}
TY - JOUR AU - Bertoluzza, Silvia AU - Pennacchio, Micol AU - Prud’homme, Christophe AU - Samake, Abdoulaye TI - Substructuring preconditioners for $h - p$ Mortar FEM JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 1057 EP - 1082 VL - 50 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2015065/ DO - 10.1051/m2an/2015065 LA - en ID - M2AN_2016__50_4_1057_0 ER -
%0 Journal Article %A Bertoluzza, Silvia %A Pennacchio, Micol %A Prud’homme, Christophe %A Samake, Abdoulaye %T Substructuring preconditioners for $h - p$ Mortar FEM %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 1057-1082 %V 50 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2015065/ %R 10.1051/m2an/2015065 %G en %F M2AN_2016__50_4_1057_0
Bertoluzza, Silvia; Pennacchio, Micol; Prud’homme, Christophe; Samake, Abdoulaye. Substructuring preconditioners for $h - p$ Mortar FEM. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 4, pp. 1057-1082. doi : 10.1051/m2an/2015065. http://archive.numdam.org/articles/10.1051/m2an/2015065/
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