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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((Δt) 2-α +N -r ) is proved for the (r-1)th-order finite element method (r2).
MSC:
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)
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