Abstract
In this paper we develop and investigate numerical algorithms for solving the fractional powers of discrete elliptic operators \({\mathcal A}_h^\alpha U = F\), 0 < α < 1, for F ∈ V h with V h a finite element or finite difference approximation space. Our goal is to construct efficient time stepping schemes for the implementation of the method based on the solution of a pseudo-parabolic problem. The second and fourth order approximations are constructed by using two- and three-level schemes. In order to increase the accuracy of approximations the geometric graded time grid is constructed which compensates the singular behavior of the solution for t close to 0. This apriori adaptive grid is compared with aposteriori adaptive grids. Results of numerical experiments are presented, they agree well with the theoretical results.
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Čiegis, R., Vabishchevich, P. (2021). High-Order Two and Three Level Schemes for Solving Fractional Powers of Elliptic Operators. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_27
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DOI: https://doi.org/10.1007/978-3-030-55874-1_27
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