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

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

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 497-505 from Springer

Abstract: 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.

Keywords: Projection Space; Element Space; Local Projection; Finite Element Space; Optimal Error Estimate (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-11795-4_53

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DOI: 10.1007/978-3-642-11795-4_53

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