Special Colloquium
Johnny Guzman
University of Minnesota
Superconvergent discontinuous Galerkin methods for second-order elliptic problems
Abstract: We identify discontinuous Galerkin methods for second-order elliptic problems having superconvergence properties similar to those of
the Raviart-Thomas and the Brezzi-Douglas-Marini mixed methods. These methods use polynomials of degree k for both the potential as well as the
flux. We show that the approximate flux converges with the optimal order of k+1, and that the approximate potential and its numerical trace
superconverge, to suitably chosen projections of the potential, with order k+2. We also apply an element-by-element postprocessing of the approximate
solution to obtain a new approximation of the potential. The new approximate solution of the potential converges with order k+2. We provide
numerical experiments that support our theoretical results.
Monday December 3, 2007 at 4:00 PM in SEO 636