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A continuous finite element method with face penalty to approximate Friedrichs' systems

Published online by Cambridge University Press:  26 April 2007

Erik Burman  and
Alexandre Ern
Erik Burman
Affiliation:
Department of Mathematics, École Polytechnique Fédérale de Lausanne, Switzerland. erik.burman@epfl.ch
Alexandre Ern
Affiliation:
CERMICS, École des ponts, ParisTech, Champs sur Marne, 77455 Marne la Vallée Cedex 2, France. ern@cermics.enpc.fr
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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.

Keywords

Finite elementsinterior penaltystabilization methodsFriedrichs' systemsfirst-order PDE's.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 1 , January 2007 , pp. 55 - 76
Copyright
© EDP Sciences, SMAI, 2007

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