Discontinuous Galerkin method with arbitrary polygonal finite elements

High-Order Discontinuous Galerkin Method on Hexahedral Elements for Aeroacoustics High-Order Discontinuous Galerkin Method on Hexahedral Elements for Aeroacoustics

Arbitrary High-order Discontinuous Galerkin Method for Electromagnetic Field Problems

In this paper, we present a time integration scheme applied to the Discontinuous Galerkin finite element method (DG-FEM, [1]) for the computation of electromagnetic fields in the interior of three-dimensional structures. This approach is also known as Arbitrary High-Order Derivative Discontinuous Galerkin (ADER-DG, [2, 3]). By this method, we reach arbitrary high accuracy not only in space but ...

Conforming polygonal finite elements

In this paper, conforming finite elements on polygon meshes are developed. Polygonal finite elements provide greater flexibility in mesh generation and are better-suited for applications in solid mechanics which involve a significant change in the topology of the material domain. In this study, recent advances in meshfree approximations, computational geometry, and computer graphics are used to...

Arbitrary order BEM-based Finite Element Method on polygonal meshes

Polygonal meshes show up in more and more applications and the BEMbased Finite Element Method turned out to be a forward-looking approach. The method uses implicitly defined trial functions, which are treated locally by means of Boundary Element Methods (BEM). Due to this choice the BEM-based FEM is applicable on a variety of meshes including hanging nodes. The aim of this presentation is to gi...

Arbitrary High Order Discontinuous Galerkin Schemes

In this paper we apply the ADER one step time discretization to the Discontinuous Galerkin framework for hyperbolic conservation laws. In the case of linear hyperbolic systems we obtain a quadrature-free explicit single-step scheme of arbitrary order of accuracy in space and time on Cartesian and triangular meshes. The ADERDG scheme does not need more memory than a first order explicit Euler ti...