A generalized finite element method for the strongly damped wave equation with rapidly varying data
| Autor: | Axel Målqvist, Per Ljung, Anna Persson |
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| Rok vydání: | 2021 |
| Předmět: |
Numerical Analysis
Steady state Applied Mathematics Mathematical analysis Phase (waves) Numerical Analysis (math.NA) 010103 numerical & computational mathematics Damped wave 01 natural sciences Finite element method 010101 applied mathematics Computational Mathematics Modeling and Simulation Convergence (routing) FOS: Mathematics Order (group theory) Orthogonal decomposition Mathematics - Numerical Analysis Transient (oscillation) 0101 mathematics Analysis Mathematics |
| Zdroj: | ESAIM: Mathematical Modelling and Numerical Analysis. 55:1375-1404 |
| ISSN: | 1290-3841 0764-583X |
| DOI: | 10.1051/m2an/2021023 |
| Popis: | We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced in Målqvist and Peterseim [Math. Comp. 83 (2014) 2583–2603], and is designed to handle independent variations in both the damping and the wave propagation speed respectively. The method does so by automatically correcting for the damping in the transient phase and for the propagation speed in the steady state phase. Convergence of optimal order is proven in L2(H1)-norm, independent of the derivatives of the coefficients. We present numerical examples that confirm the theoretical findings. |
| Databáze: | OpenAIRE |
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