Numerical Analysis Seminar

Wednesday, December 12, 2007

Speaker: Johnny Guzman, IMA (INSTITUTE FOR MATHEMATICS AND ITS APPLICATIONS)
Title: Superconvergent discontinuous Galerkin methods for second-order elliptic problems
Time: 3:00-4:00 pm
Place: Blocker 628

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 element-by-element postprocessings of the approximate solution to obtain new approximations of the potential. The new approximate solution of the potential converges with order k+2. We provide numerical experiments that support our theoretical results.

Last revised: 11/14/07 By: abnersg@math