A priori and a posteriori analysis of non-conforming finite elements with face penalty for advection-diffusion equations

El Alaoui, L, Ern, A and Burman, E (2007) A priori and a posteriori analysis of non-conforming finite elements with face penalty for advection-diffusion equations. IMA Journal of Numerical Analysis, 27 (1). pp. 151-171. ISSN 0272-4979

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Abstract

We analyse a non-conforming finite-element method to approximate advectiondiffusionreaction equations. The method is stabilized by penalizing the jumps of the solution and those of its advective derivative across mesh interfaces. The a priori error analysis leads to (quasi-)optimal estimates in the mesh size (sub-optimal by order in the L2-norm and optimal in the broken graph norm for quasi-uniform meshes) keeping the Pclet number fixed. Then, we investigate a residual a posteriori error estimator for the method. The estimator is semi-robust in the sense that it yields lower and upper bounds of the error which differ by a factor equal at most to the square root of the Pclet number. Finally, to illustrate the theory we present numerical results including adaptively generated meshes.

Item Type: Article
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Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
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    SWORD Depositor: Unset
    Depositing User: Erik Burman
    Date Deposited: 06 Feb 2012 18:12
    Last Modified: 25 Apr 2012 13:47
    URI: http://sro.sussex.ac.uk/id/eprint/15251
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