Discontinuous Galerkin Method for Convection-Diffusion Equations

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


In this section we discuss the discontinuous Galerkin method for time-dependent convection-diffusion equations
$$ u_t + \sum\limits_{i = 1}^d {f_i (u)_{x_i } } - \sum\limits_{i = 1}^d {\sum\limits_{j = 1}^d {\left( {a_{ij} \left( u \right)u_{x_j } } \right)_{x_i } = 0,} } $$
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].


Discontinuous Galerkin Method Polynomial Space Piecewise Polynomial Local Solvability Local Discontinuous Galerkin 
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© Birkhäuser Verlag 2009

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