演講訊息 TALKS

In the presentation we will first give an introduction to the discontinuous Galerkin (DG) method, which is a finite element method suitable for solving convection dominated partial differential equations (PDEs). This method has gained a lot of popularity in recent years because of its nice mathematical properties in stability and convergence, its flexibility to many different PDEs from applications, and its efficiency for adaptivity and parallel implementation. In the second part of the talk we will describe our recent work on a class of new limiters, called WENO (weighted essentially non-oscillatory) type limiters, for Runge-Kutta discontinuous Galerkin (RKDG) methods. The goal of designing such limiters is to obtain a robust and high order limiting procedure to simultaneously obtain uniform high order accuracy and sharp, non-oscillatory shock transition for the RKDG method. We adopt the following framework: first we identify the "troubled cells", namely those cells which might need the limiting procedure; then we replace the solution polynomials in those troubled cells by reconstructed polynomials using WENO methodology which maintain the original cell averages (conservation), have the same orders of accuracy as before, but are less oscillatory. These methods work quite well in our numerical tests for both one and two dimensional cases, which will be shown in the presentation.