| Speaker: | Alexandre Ern, Cermics, Ecole Nationale des Ponts et Chaussees |
| Title: | Approximation of Friedrichs' systems by continuous and discontinuous finite elements |
| Time: | 3:00-4:00 pm |
| Place: | Blocker 628 |
Friedrichs' systems are systems of first-order PDE's endowed with a symmetry and a positivity property. At the continuous level, a new formulation of boundary conditions is proposed to guarantee existence and uniqueness of solutions to these systems in the graph space. Then, a unified analysis of Discontinuous Galerkin methods to approximate Friedrichs' systems is presented. The method is formulated in terms of interface operators to penalize inter-element jumps and boundary operators to enforce boundary conditions weakly. Finally, a continuous finite element method stabilized by penalizing the inter-element jumps of the gradient of the discrete solution is proposed and analyzed. Examples of continuous and discontinuous finite element approximations are presented for advection--reaction equations, advection--diffusion--reaction equations, and the Maxwell equations in the so-called elliptic regime.
Last revised: 01/04/06 By: sgkim@math.tamu.edu