So far, we have only considered problems with first order spatial derivatives (e.g., as in conservation laws), and shown the methods to perform well and in agreement with the strong theoretical foundation. It is natural to ask whether one can extend the formulation to include more general problem types. This is the topic of this chapter and, as we will see shortly, the generalization to deal with higher-order spatial operators is less direct than one would expect. Let us consider the following simple example, taken from .
KeywordsHeat Equation Discontinuous Galerkin Discontinuous Galerkin Method Sparsity Pattern Discrete Operator
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