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We have extended Cosmos++, a multi-dimensional unstructured adaptive meshcode for solving the covariant Newtonian and general relativistic radiationmagnetohydrodynamic (MHD) equations, to accommodate both discrete finite volumeand arbitrarily high order finite element structures. The new finite elementimplementation, called CosmosDG, is based on a discontinuous Galerkin (DG)formulation, using both entropy-based artificial viscosity and slope limitingprocedures for regularization of shocks. High order multi-stage forward Eulerand strong stability preserving Runge-Kutta time integration options complementhigh order spatial discretization. We have also added flexibility in the codeinfrastructure allowing for both adaptive mesh and adaptive basis orderrefinement to be performed separately or simultaneously in a local(cell-by-cell) manner. We discuss in this report the DG formulation and presenttests demonstrating the robustness, accuracy, and convergence of our numericalmethods applied to special and general relativistic MHD, though we note anequivalent capability currently also exists in CosmosDG for Newtonian systems.

CosmosDG: An hp-Adaptive Discontinuous Galerkin Code for Hyper-Resolved Relativistic MHD