Identifier: 2009-2
Author(s): Y. Xu and C.-W. Shu
Title: Local discontinuous Galerkin methods for high-order time-dependent partial differential equations
Page count: 57 pp.
Date: 2009-02-01
Abstract:
Discontinuous Galerkin (DG) methods are a class of finite element methods using completely discontinuous basis functions, which are usually chosen as piece- wise polynomials. Since the basis functions can be completely discontinuous, these methods have the flexibility which is not shared by typical finite element methods, such as the allowance of arbitrary triangulation with hanging nodes, complete free- dom in changing the polynomial degrees in each element independent of that in the neighbors ( p adaptivity), and extremely local data structure and the resulting embar- rassingly high parallel efficiency. In this paper, we give a general review of the local DG (LDG) methods for solving high-order time-dependent partial differential equa- tions (PDEs). The important ingredient of the design of LDG schemes, namely the adequate choice of numerical fluxes, will be highlighted. Some of the applications of the LDG methods for high-order time-dependent PDEs will also be discussed.
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