Abstract
In this work, an r-linearly converging adaptive solver is constructed for parabolic evolution equations in a simultaneous space-time variational formulation. Exploiting the product structure of the space-time cylinder, the family of trial spaces that we consider are given as the spans of wavelets-in-time and (locally refined) finite element spaces-in-space. Numerical results illustrate our theoretical findings.
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The second and third authors have been supported by the Netherlands Organization for Scientific Research (NWO) under contract. no. 613.001.652
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Communicated by: Peter Benner
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Stevenson, R., van Venetië, R. & Westerdiep, J. A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations. Adv Comput Math 48, 17 (2022). https://doi.org/10.1007/s10444-022-09930-w
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DOI: https://doi.org/10.1007/s10444-022-09930-w
Keywords
- Space-time variational formulations of parabolic PDEs
- Quasi-best approximations
- Least squares methods
- Adaptive approximation
- Tensor product approximation
- Optimal preconditioners