Performances of Hybridized-, Embedded-, and Weighted-Interior Penalty Discontinuous Galerkin Methods for Heterogeneous and Anisotropic Diffusion Problems - Etangsale, Grégory; Fontaine, Vincent; Rajaonison, Nalitiana (Frontiers in Water, 2021)
The present paper discusses families of Interior Penalty Discontinuous Galerkin (IP) methods for solving heterogeneous and anisotropic diffusion problems. Specifically, we focus on distinctive schemes, namely the Hybridized-, Embedded-, and Weighted-IP schemes, leading to final matrixes of different sizes and sparsities. Hybridized- and Embedded-IP schemes are eligible for static condensation, and the globally coupled degrees of freedom are located on the mesh skeleton. In contrast, they are located inside the partition elements for the Weighted-IP variant. For a given mesh, it is well-known that the number of degrees of freedom in the element interior increases more rapidly than the degrees of freedom located on the element boundaries. We then quantify its impact on the computational performance of the different classes of IP methods in terms of accuracy and CPU time. To this aim, numerical experiments are investigated in the presence of severe anisotropies and heterogeneities. We analyze the fixed error tolerance versus the run time and mesh size to guide our performance criterion. We also outlined some relationships between these Interior Penalty schemes.