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Discontinuous Galerkin Method for Convection-Diffusion Equations

Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)

Abstract

In this section we discuss the discontinuous Galerkin method for time-dependent convection-diffusion equations
$$ u_t + \sum\limits_{i = 1}^d {f_i (u)_{x_i } } - \sum\limits_{i = 1}^d {\sum\limits_{j = 1}^d {\left( {a_{ij} \left( u \right)u_{x_j } } \right)_{x_i } = 0,} } $$
(4.1)
where (a ij (u)) is a symmetric, semi-positive definite matrix. There are several different formulations of discontinuous Galerkin methods for solving such equations, e.g., [1, 4, 6, 29, 45], however in this section we will only discuss the local discontinuous Galerkin (LDG) method [16].

Keywords

Discontinuous Galerkin Method Polynomial Space Piecewise Polynomial Local Solvability Local Discontinuous Galerkin 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag 2009

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