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

[摘要] 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(MN3 + (MN)-N-2) by a direct solver to O(MN log(MN)) per Krylov subspace iteration and a memory requirement from O(MN2) to O(N log M). An error estimate is proved. Numerical results are presented to show the utility of the method. (C) 2019 Elsevier B.V. All rights reserved.

[发布日期] 2019-12-15

[效力级别]  Proceedings Paper

[关键词] Space-time fractional diffusion equation;Directional fractional diffusion;Finite element method;Error estimate