| 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 |
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