Burman, E;
Ern, A;
(2007)
A continuous finite element method with face penalty to approximate Friedrichs' systems.
ESAIM: Mathematical Modelling and Numerical Analysis
, 41
(1)
55 - 76.
10.1051/m2an:2007007.
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Abstract
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 ½ convergence rates in the L2-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.
| Type: | Article |
|---|---|
| Title: | A continuous finite element method with face penalty to approximate Friedrichs' systems |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1051/m2an:2007007 |
| Publisher version: | http://dx.doi.org/10.1051/m2an:2007007 |
| Language: | English |
| Additional information: | © EDP Sciences, SMAI, 2007. The original publication is available at www.esaimm2an.org. |
| Keywords: | finite elements, interior penalty, stabilization methods, Friedrichs' systems, first-order PDE's |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/1384707 |
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