A priori and a posteriori analysis of non-conforming finite elements with face penalty for advection-diffusion equations |
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Authors: | El Alaoui L; Ern A; Burman E |
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Institution: |
1 Department of Mathematics, Imperial College, London, SW7 2AZ, UK and CERMICS, Ecole nationale des ponts et chaussées, Champs sur Marne, 77455 Marne la Vallée Cedex 2, France, 2 CERMICS, Ecole nationale des ponts et chaussées, Champs sur Marne, 77455 Marne la Vallée Cedex 2, France, 3 Institut d'Analyse et de Calcul Scientifique (CMCS/IACS), Ecole Polytechnique Fédérale de Lausanne, Switzerland
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Abstract: | ** Corresponding author. Email: l.elalaoui{at}imperial.ac.uk*** Email: ern{at}cermics.enpc.fr**** Email: erik.burman{at}epfl.ch
We analyse a non-conforming finite-element method to approximateadvectiondiffusionreaction equations. The methodis stabilized by penalizing the jumps of the solution and thoseof its advective derivative across mesh interfaces. The a priorierror analysis leads to (quasi-)optimal estimates in the meshsize (sub-optimal by order in the L2-norm and optimal in thebroken graph norm for quasi-uniform meshes) keeping the Pécletnumber fixed. Then, we investigate a residual a posteriori errorestimator for the method. The estimator is semi-robust in thesense that it yields lower and upper bounds of the error whichdiffer by a factor equal at most to the square root of the Pécletnumber. Finally, to illustrate the theory we present numericalresults including adaptively generated meshes. |
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Keywords: | non-conforming finite elements face penalty advection diffusion a posteriori error estimator adaptive meshes |
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