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An Adaptive Wavelet Method for Solving High-Dimensional Elliptic PDEs
- Source :
- Constructive Approximation, 30(3), 423-455. Springer New York
- Publication Year :
- 2009
- Publisher :
- Springer Science and Business Media LLC, 2009.
-
Abstract
- Adaptive tensor product wavelet methods are applied for solving Poisson’s equation, as well as anisotropic generalizations, in high space dimensions. It will be demonstrated that the resulting approximations converge in energy norm with the same rate as the best approximations from the span of the best N tensor product wavelets, where moreover the constant factor that we may lose is independent of the space dimension n. The cost of producing these approximations will be proportional to their length with a constant factor that may grow with n, but only linearly.
Details
- ISSN :
- 14320940 and 01764276
- Volume :
- 30
- Database :
- OpenAIRE
- Journal :
- Constructive Approximation
- Accession number :
- edsair.doi.dedup.....9c9fd8d7c4ccb0a76a613c6a68f05c4d