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

Superconvergence of linear functionals by discontinuous Galerkin approximations

Bernardo Cockburn, Drew Ichikawa*
University of Minnesota, School of Mathematics, Minneapolis, MN 55455, USA

  Full Text
We present a method for obtaining superconvergent approximations of linear functionals. We present an illustration of this idea in the framework of convection-diffusion equations. We use the approximation given by the discontinuous Galerkin method with polynomials of degree k. Instead of the classical order of convergence of 2k, we prove that we can obtain an approximation of order 4k. Numerical results that confirm this theoretical finding are presented.

Keywords:  Convection–diffusion equation; Discontinuous Galerkin methods; Finite element methods; Functionals; Post-processing; Superconvergence

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