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Volume 7, Issue 1
Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations

Yan Xu & Chi-Wang Shu

Commun. Comput. Phys., 7 (2010), pp. 1-46.

Published online: 2010-07

[An open-access article; the PDF is free to any online user.]

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  • Abstract

Discontinuous Galerkin (DG) methods are a class of finite element methods using discontinuous basis functions, which are usually chosen as piecewise polynomials. Since the basis functions can be 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, less restriction in changing the polynomial degrees in each element independent of that in the neighbors (p adaptivity), and local data structure and the resulting 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 equations (PDEs). The important ingredient of the design of LDG schemes, namely the adequate choice of numerical fluxes, is highlighted. Some of the applications of the LDG methods for high-order time-dependent PDEs are also be discussed.

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@Article{CiCP-7-1, author = {}, title = {Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations}, journal = {Communications in Computational Physics}, year = {2010}, volume = {7}, number = {1}, pages = {1--46}, abstract = {

Discontinuous Galerkin (DG) methods are a class of finite element methods using discontinuous basis functions, which are usually chosen as piecewise polynomials. Since the basis functions can be 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, less restriction in changing the polynomial degrees in each element independent of that in the neighbors (p adaptivity), and local data structure and the resulting 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 equations (PDEs). The important ingredient of the design of LDG schemes, namely the adequate choice of numerical fluxes, is highlighted. Some of the applications of the LDG methods for high-order time-dependent PDEs are also be discussed.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2009.09.023}, url = {http://global-sci.org/intro/article_detail/cicp/7618.html} }
TY - JOUR T1 - Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations JO - Communications in Computational Physics VL - 1 SP - 1 EP - 46 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/10.4208/cicp.2009.09.023 UR - https://global-sci.org/intro/article_detail/cicp/7618.html KW - AB -

Discontinuous Galerkin (DG) methods are a class of finite element methods using discontinuous basis functions, which are usually chosen as piecewise polynomials. Since the basis functions can be 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, less restriction in changing the polynomial degrees in each element independent of that in the neighbors (p adaptivity), and local data structure and the resulting 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 equations (PDEs). The important ingredient of the design of LDG schemes, namely the adequate choice of numerical fluxes, is highlighted. Some of the applications of the LDG methods for high-order time-dependent PDEs are also be discussed.

Yan Xu & Chi-Wang Shu. (2020). Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations. Communications in Computational Physics. 7 (1). 1-46. doi:10.4208/cicp.2009.09.023
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