An Error Estimate of a Eulerian-Lagrangian Localized Adjoint Method for a Space-Fractional Advection Diffusion Equation
Year: 2020
Author: Tingting Wang, Xiaofan Li, Hong Wang
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 2 : pp. 151–171
Abstract
We derive a Eulerian-Lagrangian localized adjoint method (ELLAM) for a space-fractional advection diffusion equation that includes a fractional Laplacian operator for modeling such application as a superdiffusive advective transport. The method symmetrizes the numerical scheme and generates accurate numerical solutions even if large time steps and relatively coarse grid meshes are used. We also study the structure of the stiffness matrix to further reduce the computational complexity and memory requirement. We prove an error estimate for the ELLAM. Numerical experiments are presented to show the potential of the method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2020-IJNAM-13645
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 2 : pp. 151–171
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Space-fractional advection diffusion fractional Laplacian characteristic method error estimate superdiffusive transport.