A Local Discontinuous Galerkin Method for Two-Dimensional Time Fractional Difusion Equations

doi:10.1007/s42967-020-00065-7

摘要/Abstract

摘要： For two-dimensional (2D) time fractional difusion equations, we construct a numerical method based on a local discontinuous Galerkin (LDG) method in space and a fnite diference scheme in time. We investigate the numerical stability and convergence of the method for both rectangular and triangular meshes and show that the method is unconditionally stable. Numerical results indicate the efectiveness and accuracy of the method and confrm the analysis.

关键词: Two-dimensional (2D) time fractional difusion equation, Local discontinuous Galerkin method (LDG), Numerical stability, Convergence analysis

Abstract: For two-dimensional (2D) time fractional difusion equations, we construct a numerical method based on a local discontinuous Galerkin (LDG) method in space and a fnite diference scheme in time. We investigate the numerical stability and convergence of the method for both rectangular and triangular meshes and show that the method is unconditionally stable. Numerical results indicate the efectiveness and accuracy of the method and confrm the analysis.

Key words: Two-dimensional (2D) time fractional difusion equation, Local discontinuous Galerkin method (LDG), Numerical stability, Convergence analysis

中图分类号:

65M60
65M12

Somayeh Yeganeh, Reza Mokhtari, Jan S. Hesthaven. A Local Discontinuous Galerkin Method for Two-Dimensional Time Fractional Difusion Equations[J]. Communications on Applied Mathematics and Computation, 2020, 2(4): 689-709.

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