Many evolution problems in physics are described by partial differential equations on an
infinite domain; therefore, one is interested in the solutions to such problems for a given …

We introduce a new relativistic astrophysics code, SpECTRE, that combines a discontinuous
Galerkin method with a task-based parallelism model. SpECTRE's goal is to achieve more …

In this paper we develop a new well-balanced discontinuous Galerkin (DG) finite element
scheme with subcell finite volume (FV) limiter for the numerical solution of the Einstein–Euler …

We present a strongly hyperbolic first-order formulation of the Einstein equations based on
the conformal and covariant Z4 system (CCZ4) with constraint-violation damping, which we …

In this paper we propose an extension of the generalized Lagrangian multiplier method
(GLM) of Munz et al.[52],[30], which was originally conceived for the numerical solution of the …

In this paper, we present a new explicit second-order accurate structure-preserving finite
volume scheme for the first-order hyperbolic reformulation of the Navier–Stokes–Korteweg …

Discontinuous Galerkin (DG) methods coupled to weighted essentially nonoscillatory
(WENO) algorithms allow high order convergence for smooth problems and for the …

The DG algorithm is a powerful method for solving pdes, especially for evolution equations
in conservation form. Since the algorithm involves integration over volume elements, it is not …

The Einstein and Maxwell equations are both systems of hyperbolic equations which need
to satisfy a set of elliptic constraints throughout evolution. However, while electrodynamics …

Discontinuous Galerkin methods are popular because they can achieve high order where
the solution is smooth, because they can capture shocks while needing only nearest …