title: Leapfrog/finite element method for fractional diffusion equation.
abstract: We analyze a fully discrete leapfrog/Galerkin finite element method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation. The generalized fractional derivative spaces are defined in a bounded interval. And some related properties are further discussed for the following finite element analysis. Then the fractional diffusion equation is discretized in space by the finite element method and in time by the explicit leapfrog scheme. For the resulting fully discrete, conditionally stable scheme, we prove an L (2)-error bound of finite element accuracy and of second order in time. Numerical examples are included to confirm our theoretical analysis.
authors: Department of Fundamental Courses, Shanghai Customs College, Shanghai 201204, China.
authors: Zhengang
authors: Z
authors: Zhao
authors: School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, China.
authors: Yunying
authors: Y
authors: Zheng
mesh_terms: D000465:Algorithms; D020342:Finite Element Analysis