A finite element method for space-time directional fractional diffusion partial differential equations in the plane and its error analysis

Abstract 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.

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