期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 35, 期 3, 页码 A1233-A1253出版社
SIAM PUBLICATIONS
DOI: 10.1137/120890144
关键词
discontinuous Galerkin; Gauss-Lobatto spectral element; summation-by-parts; energy stability; simultaneous approximation term; nonlinear conservation law; discrete conservation; split operator formulation; skew symmetric
资金
- Deutsche Forschungsgemeinschaft (DFG)
- cluster of excellence Simulation Technology (SimTech), Universitat Stuttgart
This paper shows that the discontinuous Galerkin collocation spectral element method with Gauss-Lobatto points (DGSEM-GL) satisfies the discrete summation-by-parts (SBP) property and can thus be classified as an SBP-SAT (simultaneous approximation term) scheme with a diagonal norm operator. In the same way, SBP-SAT finite difference schemes can be interpreted as discontinuous Galerkin-type methods with a corresponding weak formulation based on an inner-product formulation common in the finite element community. This relation allows the use of matrix-vector notation (common in the SBP-SAT finite difference community) to show discrete conservation for the split operator formulation of scalar nonlinear conservation laws for DGSEM-GL and diagonal norm SBP-SAT. Based on this result, a skew-symmetric energy stable discretely conservative DGSEM-GL formulation (applicable to general diagonal norm SBP-SAT schemes) for the nonlinear Burgers equation is constructed.
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