A continuous finite element method with face penalty to approximate Friedrichs' systems
Department of Mathematics, École Polytechnique Fédérale
de Lausanne, Switzerland. firstname.lastname@example.org
2 CERMICS, École des ponts, ParisTech, Champs sur Marne, 77455 Marne la Vallée Cedex 2, France. email@example.com
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.
Mathematics Subject Classification: 65N30 / 65N12 / 74S05 / 78M10 / 76R99 / 35F15
Key words: Finite elements / interior penalty / stabilization methods / Friedrichs' systems / first-order PDE's.
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