Publication: Finite elements for elliptic problems with highly varying, nonperiodic diffusion matrix
Finite elements for elliptic problems with highly varying, nonperiodic diffusion matrix
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Peterseim, D., & Sauter, S. (2012). Finite elements for elliptic problems with highly varying, nonperiodic diffusion matrix. Multiscale Modeling & Simulation, 10(3), 665–695. https://doi.org/10.1137/10081839X
Abstract
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This paper considers the numerical solution of elliptic boundary value problems with a complicated (nonperiodic) diffusion matrix which is smooth but highly oscillating on very different scales. We study the influence of the scales and amplitudes of these oscillations to the regularity of the solution. We introduce weighted Sobolev norms of integer order, where the (p + 1)st seminorm is weighted by properly scaled pth derivative of the diffusion coefficient. The constants in the regularity estimates then turn out to depend only on glo
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- Peterseim, D
- Sauter, Stefan
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Peterseim, D., & Sauter, S. (2012). Finite elements for elliptic problems with highly varying, nonperiodic diffusion matrix. Multiscale Modeling & Simulation, 10(3), 665–695. https://doi.org/10.1137/10081839X
