Geodesic
A continuous finite element method with face penalty to approximate Friedrichs' systems
Burman, Erik1  ; Ern, Alexandre 
1 Ecole Polytechnique Federale Institute of Analysis and Scientific Computing CH-1015 Lausanne Switzerland
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 1, pp. 55-76

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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 1 2 convergence rates in the L 2 -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.

DOI : 10.1051/m2an:2007007
Classification : 65N30, 65N12, 74S05, 78M10, 76R99, 35F15
Keywords: finite elements, interior penalty, stabilization methods, Friedrichs' systems, first-order PDE's

Burman, Erik 1 ; Ern, Alexandre 

1 Ecole Polytechnique Federale Institute of Analysis and Scientific Computing CH-1015 Lausanne Switzerland 
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     title = {A continuous finite element method with face penalty to approximate {Friedrichs'} systems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
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Burman, Erik; Ern, Alexandre. A continuous finite element method with face penalty to approximate Friedrichs' systems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 1, pp. 55-76. doi: 10.1051/m2an:2007007

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