Stability and Functional Superconvergence of Narrow-Stencil Second-Derivative Generalized Summation-By-Parts Discretizations
| Autor: | Worku, Zelalem Arega, Zingg, David W. |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Journal of Scientific Computing, 90:42 (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s10915-021-01707-5 |
| Popis: | We analyze the stability and functional superconvergence of discretizations of diffusion problems with the narrow-stencil second-derivative generalized summation-by-parts (SBP) operators coupled with simultaneous approximation terms (SATs). Provided that the primal and adjoint solutions are sufficiently smooth and the SBP-SAT discretization is primal and adjoint consistent, we show that linear functionals associated with the steady diffusion problem superconverge at a rate of $ 2p $ when a degree $ p+1 $ narrow-stencil or a degree $ p $ wide-stencil generalized SBP operator is used for the spatial discretization. Sufficient conditions for stability of adjoint consistent discretizations with the narrow-stencil generalized SBP operators are presented. The stability analysis assumes nullspace consistency of the second-derivative operator and the invertibility of the matrix approximating the first derivative at the element boundaries. The theoretical results are verified by numerical experiments with the one-dimensional Poisson problem. Comment: 21 pages, 8 figures |
| Databáze: | arXiv |
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