报告题目：LDG methods for nonlinear equations and DDG methods for elliptic interface problems
报告人：Jue YAN （Iowa State University ）
For the first part of the talk, we use a modified Buckley-Leverett equation to explain the idea of Local discontinuous Galerkin (LDG) method. We show how to choose numerical fluxes to obtain stability of the numerical solution for strong nonlinear PDEs with LDG methods. We also discuss the study of LDG method for nonlinear Hamilton-Jacobi equations.
For the second part, we review the direct discontinuous Galerkin (DDG) method and its variations, namely the DDGIC and symmetric DDG methods. Compared to the leading diffusion DG method solvers like the interior penalty method (SIPG), we find out our diffusion solver the DDG methods have many advantages. Under the topic of maximum principle, DDG methods numerical solution can be proved to satisfy strict maximum principle even on unstructured triangular mesh with at least third order of accuracy. Recently we develop DDG methods to solve Keller-Segel Chemotaxis equations. We find out that the DDGIC or symmetric DDG methods have the hidden super convergence property on its approximation to the solution gradients. In the end we discuss our studies of symmetric DDG methods on elliptic interface problems