Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Superconvergence of the local discontinuous Galerkin method applied to diffusion problems

S. Adjerid*, D. Issaev
Virginia Tech, Department of Mathematics, Blacksburg, VA 24061, USA
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ABSTRACT
We present new superconvergence results for the local discontinuous Galerkin method applied to transient diffusion problems and examine the effect of numerical fluxes on superconvergence. We show that the gradient of the p-degree discontinuous finite element solution is superconvergent at the roots of the derivative of (p + 1)-degree Radau polynomial.

Keywords:  Superconvergence; Finite elements; Discontinuous Galerkin; Diffusion problems
* Corresponding author. Tel.: +1 540 231 5945; Fax: +1 540 231 5960; E-mail: adjerids@math.vt.edu