Speaker：Jianfang Lu（South China University of Technology）

Time：2022-12-02, 15:00

Location：Tencent Meeting ID：800-110-721（No Password）

Abstract:

In this talk, we propose an oscillation-free discontinuous Galerkin (OFDG) method to control the spurious oscillations when solving the hyperbolic conservation laws. Usually, the high order linear numerical schemes would generate spurious oscillations when the solution contains discontinuities. The spurious oscillations maybe harmful to the numerical simulation, as it not only generates some artificial structures not belonging to the problems, but also causes many overshoots and undershoots that make the numerical scheme less robust. To overcome this difficulty, we introduce a numerical damping term to control spurious oscillations based on the classic DG formulation. Comparing to the classic DG method, the proposed DG method still maintains many good properties, such as the extremely local data structure, conservation, $L^2$-boundedness, optimal error estimates and superconvergence. We also provide some numerical examples to show the good performance of the proposed DG scheme and verify our theoretical results.