High-order numerical methods for nonlinear PDEs

PDE Seminar
Tuesday, November 25, 2008 - 3:05pm for 1.5 hours (actually 80 minutes)
Skiles 255
Bojan Popov – Texas A&M University
Michael Westdickenberg

In this talk we will consider three different numerical methods for solving nonlinear PDEs:

  1. A class of Godunov-type second order schemes for nonlinear conservation laws, starting from the Nessyahu-Tadmor scheme;
  2. A class of L1 -based minimization methods for solving linear transport equations and stationary Hamilton- Jacobi equations;
  3. Entropy-viscosity methods for nonlinear conservation laws.

All of the above methods are based on high-order approximations of the corresponding nonlinear PDE and respect a weak form of an entropy condition. Theoretical results and numerical examples for the performance of each of the three methods will be presented.