A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations

Barrenechea, Gabriel and Volker, John and Knobloch, Petr (2013) A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations. ESAIM: Mathematical Modelling and Numerical Analysis, 47 (5). pp. 1335-1366. ISSN 0764-583X

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    Abstract

    An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steadystate and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates are derived which are supported by numerical studies. These studies demonstrate also the reduction of the spurious oscillations.