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Discontinuous Galerkin Finite Element (DGFE) methods offer a mathematicallybeautiful, computationally efficient, and efficiently parallelizable way tosolve hyperbolic partial differential equations. These properties make themhighly desirable for numerical calculations in relativistic astrophysics andmany other fields. The BSSN formulation of the Einstein equations hasrepeatedly demonstrated its robustness. The formulation is not only stable butallows for puncture-type evolutions of black hole systems. To-date no one hasbeen able to solve the full (3+1)-dimensional BSSN equations using DGFEmethods. This is partly because DGFE discretization often occurs at the levelof the equations, not the derivative operator, and partly because DGFE methodsare traditionally formulated for manifestly flux-conservative systems. Bydiscretizing the derivative operator, we generalize a particular flavor of DGFEmethods, Local DG methods, to solve arbitrary second-order hyperbolicequations. Because we discretize at the level of the derivative operator, ourmethod can be interpreted as either a DGFE method or as a finite differencesstencil with non-constant coefficients.

An Operator-Based Local Discontinuous Galerkin Method Compatible With the BSSN Formulation of the Einstein Equations