Testing Discontinuous Galerkin Methods in the Einstein Toolkit for Numerical Relativity

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Discontinuous Galerkin finite element (DGFE) methods combine advantages of both finite differences and finite elements approaches. These methods scale extremely well and they have been very successful in computational fluid dynamics. As such we would like to transpose them to the domain of relativistic astrophysics. Recently we have implemented DGFE methods in the Einstein Toolkit a large numerical relativity codebase used by hundreds of scientists around the world. However before DGFE methods can be used in production simulations we must ensure that our implementation is up to the efficiency and accuracy standards of a production codebase. Here we detail our efforts to test our implementation using the Apples with Apples tests (c.f. arXiv:gr-qc/0305023 and arXiv:0709.3559). We briefly introduce DGFE methods explain the Apples with Apples tests and our rationale for using them and discuss results.