The asymptotic stability of steady solutions of reaction-convection-diffusion equations.

F.A. Howes

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

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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...