A continuous finite element method to approximate Friedrichs’ systems is proposed and analyzed. Stability is achieved by penalizing the jumps across mesh interfaces of the normal derivative of some components of the discrete solution. The convergence analysis leads to optimal convergence rates in the graph norm and suboptimal of order convergence rates in the -norm. A variant of the method specialized to Friedrichs’ systems associated with elliptic PDE’s in mixed form and reducing the number of nonzero entries in the stiffness matrix is also proposed and analyzed. Finally, numerical results are presented to illustrate the theoretical analysis.
Keywords: finite elements, interior penalty, stabilization methods, Friedrichs' systems, first-order PDE's
Burman, Erik 1 ; Ern, Alexandre
@article{M2AN_2007__41_1_55_0,
author = {Burman, Erik and Ern, Alexandre},
title = {A continuous finite element method with face penalty to approximate {Friedrichs'} systems},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {55--76},
year = {2007},
publisher = {EDP Sciences},
volume = {41},
number = {1},
doi = {10.1051/m2an:2007007},
zbl = {1129.65083},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2007007/}
}
TY - JOUR AU - Burman, Erik AU - Ern, Alexandre TI - A continuous finite element method with face penalty to approximate Friedrichs' systems JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2007 SP - 55 EP - 76 VL - 41 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2007007/ DO - 10.1051/m2an:2007007 LA - en ID - M2AN_2007__41_1_55_0 ER -
%0 Journal Article %A Burman, Erik %A Ern, Alexandre %T A continuous finite element method with face penalty to approximate Friedrichs' systems %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 55-76 %V 41 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2007007/ %R 10.1051/m2an:2007007 %G en %F M2AN_2007__41_1_55_0
Burman, Erik; Ern, Alexandre. A continuous finite element method with face penalty to approximate Friedrichs' systems. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 1, pp. 55-76. doi: 10.1051/m2an:2007007
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