Abstract
In Ch. 12 we discussed the solution of the continuous Galerkin method for solving multi-dimensional elliptic problems. Let us now describe the solution of two-dimensional elliptic problems with the discontinuous Galerkin method. Although the extension to multi-dimensions is straightforward, to simplify the discussion we focus on two dimensions. This chapter focuses on the discretization of scalar elliptic problems (e.g., Poisson problem) using the local discontinuous Galerkin (LDG) method. We reserve the symmetric interior penalty Galerkin (SIPG) method for Ch. 14.
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Giraldo, F.X. (2020). 2D Discontinuous Galerkin Methods for Elliptic Equations. In: An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases. Texts in Computational Science and Engineering, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-030-55069-1_13
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DOI: https://doi.org/10.1007/978-3-030-55069-1_13
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