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

Gabriel Barrenechea, John Volker, Petr Knobloch

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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.
Original languageEnglish
Pages (from-to)1335-1366
Number of pages32
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume47
Issue number5
Early online date13 Mar 2013
DOIs
Publication statusPublished - 30 Jul 2013

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Keywords

  • finite element method
  • local projection stabilization
  • crosswind diffusion
  • convection-diffusion-reaction equation
  • well posedness
  • time dependent problem
  • stability
  • error estimate

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