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High-order finite element methods for time-fractional partial differential equations. (English) Zbl 1216.65130
Summary: The aim of this paper is to develop high-order methods for solving time-fractional partial differential equations. The proposed high-order method is based on a high-order finite element method for space and a finite difference method for time. An optimal convergence rate of $O((\Delta t)^{2 - \alpha }+N^{ - r})$ is proved for the $(r - 1)$th-order finite element method ($r\geq 2$).

65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M06Finite difference methods (IVP of PDE)
35K05Heat equation
35R11Fractional partial differential equations
65M12Stability and convergence of numerical methods (IVP of PDE)
Full Text: DOI
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