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crosswind diffusion

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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A local projection stabilization finite element methodwith nonlinear crosswind diffusion for convection-diffusion-reaction equations
Gabriel R. Barrenechea, Volker John, Petr Knobloch
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 47 / Issue 5 / September 2013

Published online by Cambridge University Press:

30 July 2013, pp. 1335-1366

Print publication:

September 2013
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An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steady-state 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.