In this paper we present a new approach to simulations on complex‐shaped domains. The method is based on a discontinuous Galerkin (DG) method, using trial and test functions defined on a structured grid. Essential boundary conditions are imposed weakly via the DG formulation. This method offers a discretization where the number of unknowns is independent of the complexity of the domain. We will show numerical computations for an elliptic scalar model problem in ℝ2 and ℝ3. Convergence rates for different polynomial degrees are studied.
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Bastian et al. (2009) studied this question.
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