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Stabilisation of local projection type applied to convection-diffusion problems with mixed boundary conditions

by Matthies, G., Skrzypacz, P., Tobiska, L..

Series: 2007-44, Preprints

65N12 Stability and convergence of numerical methods
65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods

We present the analysis for the local projection stabilisation applied to convection-diffusion-reaction problems with mixed boundary conditions. We concentrate on the enrichment approach of the local projection methods. Optimal a-priori error estimates will be proved. Numerical tests confirm the theoretical convergence results. Moreover, the local projection stabilisation leads to numerical schemes which work well for problems with several types of layers. Away from
layers, the solution is captured very well.

stabilised finite elements, convection-diffusion