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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 (\(r\geq 2\)).

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35R11 Fractional partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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