Non-uniform L1/discontinuous Galerkin approximation for the time-fractional convection equation with weak regular solution

Changpin Li and Zhen Wang

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 182, issue C, 838-857

Abstract: In this paper, an efficient method seeking the numerical solution of a time-fractional convection equation whose solution is not smooth at the starting time is presented. The Caputo time-fractional derivative of order in (0,1) is discretized by the L1 finite difference method using non-uniform meshes; and, for the spatial derivative the discontinuous Galerkin (DG) finite element method is used. The stability and convergence of the method are analyzed for two-dimensional domains, using Cartesian and a particular class of unstructured grids. At last, several numerical examples are carried out which support the theoretical analysis.

Keywords: Time-fractional convection equation; L1 scheme; Discontinuous Galerkin method; Rectangular element; Triangular element (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:182:y:2021:i:c:p:838-857

DOI: 10.1016/j.matcom.2020.12.007

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