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- W4281716675 abstract "We derive an equilibrated a posteriori error estimator for the space (semi) discretization of the scalar wave equation by finite elements. In the idealized setting where time discretization is ignored and the simulation time is large, we provide fully guaranteed upper bounds that are asymptotically constant-free and show that the proposed estimator is efficient and polynomial-degree-robust, meaning that the efficiency constant does not deteriorate as the approximation order is increased. To the best of our knowledge, this work is the first to propose an estimator for the wave equation that is provably reliable and efficient in the same norm. We also explain, without analysis, how the estimator is adapted to cover time discretization by an explicit time integration scheme. Numerical examples illustrate the theory and suggest that it is sharp." @default.
- W4281716675 created "2022-06-13" @default.
- W4281716675 creator A5061926880 @default.
- W4281716675 date "2023-07-10" @default.
- W4281716675 modified "2023-09-30" @default.
- W4281716675 title "Asymptotically Constant-Free and Polynomial-Degree-Robust a Posteriori Estimates for Space Discretizations of the Wave Equation" @default.
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- W4281716675 doi "https://doi.org/10.1137/22m1485619" @default.
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