Abstract
This work is concerned with the classical wave equation with a high-contrast coefficient in the spatial derivative operator. We first treat the periodic case, where we derive a new limit in the one-dimensional case. The behavior is illustrated numerically and contrasted to the higher-dimensional case. For general unstructured high-contrast coefficients, we present the Localized Orthogonal Decomposition and show a priori error estimates in suitably weighted norms. Numerical experiments illustrate the convergence rates in various settings.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: 496556642
Award Identifier / Grant number: EXC-2047/1 – 390685813
Funding statement: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under project number 496556642. The work of BV at University Bonn is also funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.
Acknowledgements
Major parts of this work were accomplished while BV was affiliated with Karlsruher Institut für Technologie (KIT) and EF conducted a research internship at KIT. We thank the anonymous reviewers for their valuable remarks which helped to improve the paper.
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
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Artikel in diesem Heft
- Frontmatter
- Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 1)
- Efficient P1-FEM for Any Space Dimension in Matlab
- Adaptive Image Compression via Optimal Mesh Refinement
- Wave Propagation in High-Contrast Media: Periodic and Beyond
- On a Mixed FEM and a FOSLS with 𝐻−1 Loads
- A Discontinuous Galerkin and Semismooth Newton Approach for the Numerical Solution of Bingham Flow with Variable Density
- A Time Splitting Method for the Three-Dimensional Linear Pauli Equation
- Simultaneous Reconstruction of Speed of Sound and Nonlinearity Parameter in a Paraxial Model of Vibro-Acoustography in Frequency Domain
- Robust PRESB Preconditioning of a 3-Dimensional Space-Time Finite Element Method for Parabolic Problems
- Nonlinear PDE Models in Semi-relativistic Quantum Physics
- Weak Convergence of the Rosenbrock Semi-implicit Method for Semilinear Parabolic SPDEs Driven by Additive Noise
- Guaranteed Lower Eigenvalue Bounds for Steklov Operators Using Conforming Finite Element Methods
- A Posteriori Error Estimation for the Optimal Control of Time-Periodic Eddy Current Problems