摘要
The aim of this paper is to develop a fully discrete local discontinuous Galerkin method to solve a class of variable-order fractional diffusion problems.The scheme is discretized by a weighted-shifted Grünwald formula in the temporal discretization and a local discontinuous Galerkin method in the spatial direction.The stability and the L^(2)-convergence of the scheme are proved for all variable-orderα(t)∈(0,1).The proposed method is of accuracy-order O(τ^(3)+h^(k+1)),whereτ,h,and k are the temporal step size,the spatial step size,and the degree of piecewise P^(k)polynomials,respectively.Some numerical tests are provided to illustrate the accuracy and the capability of the scheme.
基金
This work was supported by the Fundamental Research Funds for the Henan Provincial Colleges and Universities in Henan University of Technology(2018RCJH10)
the Training Plan of Young Backbone Teachers in Henan University of Technology(21420049)
the Training Plan of Young Backbone Teachers in Colleges and Universities of Henan Province(2019GGJS094)
the innovative Funds Plan of Henan University of Technology,Foundation of Henan Educational Committee(19A110005)
the National Natural Science Foundation of China(11861068).
