| Abstract: |
| We extend the applicability of the popular interior penalty discontinuous Galerkin (dG) method for discretising advection diffusion reaction problems to meshes comprising extremely general, essentially arbitrarily shaped elements. In particular, our analysis allows for curved element shapes without the use of iso-parametric elemental maps. The feasibility of the method relies on the definition of a suitable discontinuity penalisation parameter, which turns out to be essentially independent of the particular element shape. A priori error bounds for the resulting method are given under very mild structural assumptions restricting the magnitude of the local curvature of element boundaries. Numerical experiments are also presented, indicating the practicality of the proposed approach. This work generalises our earlier work detailed in the monograph. |
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