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

El Alaoui, L.; Ern, A.; Burman, E.
January 2007
IMA Journal of Numerical Analysis;2007, Vol. 27 Issue 1, p151
Academic Journal
We analyse a non-conforming finite-element method to approximate advection–diffusion–reaction 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 ½ in the L2-norm and optimal in the broken graph norm for quasi-uniform meshes) keeping the Péclet 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 Péclet number. Finally, to illustrate the theory we present numerical results including adaptively generated meshes.


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