Abstract
We analyze how to solve hyperbolic PDEs with compactly supported orthonormal wavelets adaptively. We use thresholded wavelet expansions of signals and operators. A tree structure is used to represent the signal, and a multidimensional analogue of the fast wavelet transform is used to expand the operators. We solve the advection equation and Burgers' equation on a periodic domain.
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Holmström, M., Waldén, J. Adaptive Wavelet Methods for Hyperbolic PDEs. Journal of Scientific Computing 13, 19–49 (1998). https://doi.org/10.1023/A:1023252610346
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DOI: https://doi.org/10.1023/A:1023252610346