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  Unified discontinuous Galerkin scheme for a large class of elliptic equations

Fischer, N., & Pfeiffer, H. P. (2022). Unified discontinuous Galerkin scheme for a large class of elliptic equations. Physical Review D, 105(2): 024034. doi:10.1103/PhysRevD.105.024034.

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 Creators:
Fischer, Nils1, Author              
Pfeiffer, Harald P.1, Author              
Affiliations:
1Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_1933290              

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Free keywords: Mathematics, Numerical Analysis, math.NA,Computer Science, Numerical Analysis, cs.NA,General Relativity and Quantum Cosmology, gr-qc, Physics, Computational Physics, physics.comp-ph
 Abstract: We present a discontinuous Galerkin internal-penalty scheme that is applicable to a large class of linear and nonlinear elliptic partial differential equations. The unified scheme can accommodate all second-order elliptic equations that can be formulated in first-order flux form, encompassing problems in linear elasticity, general relativity, and hydrodynamics, including problems formulated on a curved manifold. It allows for a wide range of linear and nonlinear boundary conditions, and accommodates curved and nonconforming meshes. Our generalized internal-penalty numerical flux and our Schur-complement strategy of eliminating auxiliary degrees of freedom make the scheme compact without requiring equation-specific modifications. We demonstrate the accuracy of the scheme for a suite of numerical test problems. The scheme is implemented in the open-source SpECTRE numerical relativity code.

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 Dates: 2021-08-122022-01-112022
 Publication Status: Published in print
 Pages: 22 pages, 13 figures, 2 tables, published version. Results are reproducible with the ancillary input files
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 Identifiers: arXiv: 2108.05826
DOI: 10.1103/PhysRevD.105.024034
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Title: Physical Review D
  Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : American Physical Society
Pages: - Volume / Issue: 105 (2) Sequence Number: 024034 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: https://pure.mpg.de/cone/journals/resource/111088197762258