hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes

Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis, Paul Houston
2016 Mathematical Modelling and Numerical Analysis  
We consider the hp-version interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the advection-diffusion-reaction equation on general computational meshes consisting of polygonal/polyhedral (polytopic) elements. In particular, new hpversion a priori error bounds are derived based on a specific choice of the interior penalty parameter which allows for edge/face-degeneration. The proposed method employs elemental polynomial bases of total degree
more » ... es of total degree p (Pp-basis) defined in the physical coordinate system, without requiring the mapping from a given reference or canonical frame. Numerical experiments highlighting the performance of the proposed DGFEM are presented. In particular, we study the competitiveness of the p-version DGFEM employing a Pp-basis on both polytopic and tensor-product elements with a (standard) DGFEM employing a (mapped) Qp-basis. Moreover, a computational example is also presented which demonstrates the performance of the proposed hp-version DGFEM on general agglomerated meshes.
doi:10.1051/m2an/2015059 fatcat:psuadnttavczrhtx4xz6yuksj4