A boundary conformal discontinuous Galerkin approach for electro-quasistatic field problems on Cartesian grids. (1st January 2014) - Fröhlcke, Annette; Gjonaj, Erion; Weiland, Thomas
A boundary conformal approach for solving three-dimensional electro-quasistatic field problems with a high order discontinuous Galerkin method on Cartesian grids is proposed. The method is based on a novel cut-cell discretisation which is applied only on elements intersected by curved material boundaries. A particular numerical quadrature is introduced which allows for an accurate integration of the high order finite element operators taking into account the exact geometry of the cut-cells. Furthermore, a general hybridisation of the cut-cell approach with the conventional finite element method in the homogeneous parts of the computational domain is proposed. Numerical examples are presented which demonstrate the accuracy of this discretisation method for practical problems with curved geometries.