| Author | Jianfeng Yan, Jason Hicken |
|---|---|
| Title | Interior Penalties for Summation-by-Parts Discretizations of Linear Second-Order Differential Equations |
| Year | 2018 |
| Journal | Journal of Scientific Computing |
| Volume | 75 |
| Pages | 1385–1414 |
| Abstract | This work focuses on simultaneous approximation terms (SATs) for multidimensional summation-by-parts (SBP) discretizations of linear second-order partial differential equations with variable coefficients. Through the analysis of adjoint consistency and stability, we present several conditions on the SAT penalties for general operators, including those operators that do not have nodes on their boundary or do not correspond with a collocation discontinuous Galerkin method. Based on these conditions, we generalize the modified scheme of Bassi and Rebay and the symmetric interior penalty Galerkin method to SBP-SAT discretizations. Numerical experiments are carried out on unstructured grids with triangular elements to verify the theoretical results. |
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| DOI Link | 10.1007/s10915-017-0591-8 |