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Local Projection Method for Convection-Diffusion-Reaction Problems with Projection Spaces Defined on Overlapping Sets

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Petr Knobloch

    (Charles University, Faculty of Mathematics and Physics, Department of Numerical Mathematics)

Abstract

We extend the local projection finite element method for steady scalar convection-diffusion-reaction equations to local projection spaces defined on overlapping sets. This enables to define the local projection method without the need of a mesh refinement or an enrichment of the finite element space. For the streamline derivative based stabilization, we introduce a modification that leads to an optimal estimate of the consistency error even if the stabilization parameters scale correctly with respect to convection, diffusion and mesh width. The main result of the paper is an optimal error estimate with respect to the standard local projection norm.

Suggested Citation

  • Petr Knobloch, 2010. "Local Projection Method for Convection-Diffusion-Reaction Problems with Projection Spaces Defined on Overlapping Sets," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 497-505, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_53
    DOI: 10.1007/978-3-642-11795-4_53
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