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A finite element method for space-time directional fractional diffusion partial differential equations in the plane and its error analysis. (English) Zbl 1422.65254

Summary: We present and analyze a fast finite element method for space-time fractional directional partial differential equations in a bounded domain in the plane. The fast solver significantly reduces the computational work of solving the discrete linear algebraic systems from \(O(M N^3 + M^2 N)\) by a direct solver to \(O(M N \log(M N))\) per Krylov subspace iteration and a memory requirement from \(O(M N^2)\) to \(O(N \log M)\). An error estimate is proved. Numerical results are presented to show the utility of the method.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
15B05 Toeplitz, Cauchy, and related matrices
35R11 Fractional partial differential equations
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