Pei Fu: High order cut discontinuous Galerkin methods for hyperbolic conservation laws in one space dimension
Time: Thu 2020-08-20 14.15 - 15.00
Location: Online talk via Zoom
Lecturer: Pei Fu, Uppsala University
In this work, we develop a family of high order cut discontinuous Galerkin (DG) methods for hyperbolic conservation laws in one space dimension. The ghost penalty stabilization is used to stabilize the scheme for small cut elements. Analysis shows that our proposed methods have similar stability and accuracy properties to the standard DG methods on a regular mesh. We also prove that the cut DG method is total variation diminishing at lower order. We use the strong stability preserving Runge-Kutta method for time discretization and the time step is independent on the size of cut element. Numerical examples demonstrate the cut DG methods are high order accurate for smooth problems and perform well for discontinuous problems.
This work is joint with Gunilla Kreiss.