We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to the right-hand side in the standard variational formulation of the problem. We prove optimal error estimates of the methods on general quasi-uniform and shape regular meshes in maximum norms. In addition, we apply the method to a Stokes interface problem, adding correction terms for the velocity and the pressure, obtaining optimal convergence results.
Accepté le :
DOI : 10.1051/m2an/2015093
Keywords: Interface problems, finite elements, pointwise estimates
Guzmán, Johnny 1 ; Sánchez, Manuel A. 1 ; Sarkis, Marcus 2
@article{M2AN_2016__50_5_1561_0,
author = {Guzm\'an, Johnny and S\'anchez, Manuel A. and Sarkis, Marcus},
title = {Higher-order finite element methods for elliptic problems with interfaces},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1561--1583},
year = {2016},
publisher = {EDP Sciences},
volume = {50},
number = {5},
doi = {10.1051/m2an/2015093},
mrnumber = {3554552},
zbl = {1353.65120},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2015093/}
}
TY - JOUR AU - Guzmán, Johnny AU - Sánchez, Manuel A. AU - Sarkis, Marcus TI - Higher-order finite element methods for elliptic problems with interfaces JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 1561 EP - 1583 VL - 50 IS - 5 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2015093/ DO - 10.1051/m2an/2015093 LA - en ID - M2AN_2016__50_5_1561_0 ER -
%0 Journal Article %A Guzmán, Johnny %A Sánchez, Manuel A. %A Sarkis, Marcus %T Higher-order finite element methods for elliptic problems with interfaces %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 1561-1583 %V 50 %N 5 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2015093/ %R 10.1051/m2an/2015093 %G en %F M2AN_2016__50_5_1561_0
Guzmán, Johnny; Sánchez, Manuel A.; Sarkis, Marcus. Higher-order finite element methods for elliptic problems with interfaces. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 5, pp. 1561-1583. doi: 10.1051/m2an/2015093
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