An unfitted finite element method using discontinuous Galerkin

Abstract 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 ℝ 2 and ℝ 3 . Convergence rates for different polynomial degrees are studied. Copyright © 2009 John Wiley & Sons, Ltd.