Notes on Discontinuous Galerkin Methods for Convection Dominated PDEs

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Published in Chengdu, Sichuan, 2019


Mathematics Genealogy Project


In these minicourses, we will give a general introduction to the discontinuous Galerkin (DG) methods for solving time-dependent, convection-dominated partial differential equations (PDEs), including the hyperbolic conservation laws, convection-diffusion equations, and PDEs containing higher-order spatial derivatives such as the KdV equations and other nonlinear dispersive wave equations.We will discuss cell entropy inequalities, nonlinear stability, and error estimates. The important ingredient of the design of DG schemes, namely the adequate choice of numerical fluxes, will be explained in detail. Issues related to the implementation of the DG method will also be addressed.

Lecture Notes


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