Adaptive piecewise constant discontinuous Galerkin methods for convection-diffusion problems
2009 (English)Manuscript (preprint) (Other academic)
In this paper we present a discontinuous Galerkin method with piecewise constant approximation for convection-diffusion type equations. We show that if the discretization is carefully chosen, then the method is optimal in the L2 norm as well as in a discrete energy norm measuring the normal flux across element boundaries. We also derive a posteriori error estimates and illustrate their effectiveness in combination with adaptive mesh refinement on a few benchmark problems.
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IdentifiersURN: urn:nbn:se:umu:diva-30254OAI: oai:DiVA.org:umu-30254DiVA: diva2:281193