A comparison of polygonal discontinuous Galerkin methods

Using a traditional finite element method on a domain with a detailed interface, will result in a significant increase of the number of elements, compared to the domain with a less detailed interface. Such increase can make the use of traditional finite element methods computationally too costly. Using Polygonal instead of triangular elements could allow the use of larger elements on the interface, thereby reducing the cost to a feasible level. We compare two finite element methods, the Agglomerated Discontinuous Galerkin and the Discontinuous Galerkin Virtual element method, as possible candidates to use on such a polygonal mesh. Additionally, we look at possibilities for efficient and accurate computation of the element vector and the L2-error.