Numerical approximation schemes for multi-dimensional wave equations in asymmetric spaces
Lescarret V, Zuazua E (2015)
Publication Type: Journal article
Publication year: 2015
Journal
Book Volume: 84
Pages Range: 119-152
Journal Issue: 291
DOI: 10.1090/s0025-5718-2014-02887-1
Abstract
We develop finite difference numerical schemes for a model arising in multi-body structures, previously analyzed by H. Koch and E. Zuazua, constituted by two n-dimensional wave equations coupled with a (n - 1)- dimensional one along a flexible interface. That model, under suitable assumptions on the speed of propagation in each media, is well-posed in asymmetric spaces in which the regularity of solutions differs by one derivative from one medium to the other. Here we consider a flat interface and analyze this property at a discrete level, for finite difference and mixed finite element methods on regular meshes parallel to the interface. We prove that those methods are well-posed in such asymmetric spaces uniformly with respect to the mesh-size parameters and we prove the convergence of the numerical solutions towards the continuous ones in these spaces. In other words, these numerical methods that are well-behaved in standard energy spaces, preserve the convergence properties in these asymmetric spaces too. These results are illustrated by several numerical experiments.
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France (FR)
Spain (ES)How to cite
APA:
Lescarret, V., & Zuazua, E. (2015). Numerical approximation schemes for multi-dimensional wave equations in asymmetric spaces. Mathematics of Computation, 84(291), 119-152. https://dx.doi.org/10.1090/s0025-5718-2014-02887-1
MLA:
Lescarret, Vincent, and Enrique Zuazua. "Numerical approximation schemes for multi-dimensional wave equations in asymmetric spaces." Mathematics of Computation 84.291 (2015): 119-152.
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