A Fast Finite Volume Method on Locally Refined Meshes for Fractional Diffusion Equations

Authors

  • Jinhong Jia School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, Shandong, China.
  • Hong Wang Department of Mathematics, University of South Carolina, SC, USA.

DOI:

https://doi.org/10.4208/eajam.271118.280319

Keywords:

Space-fractional diffusion equation, locally refined mesh, Toeplitz matrix, circulant matrix, finite volume method.

Abstract

In this work, we consider a boundary value problem involving Caputo derivatives defined in the plane. We develop a fast locally refined finite volume method for variable-coefficient conservative space-fractional diffusion equations in the plane to resolve boundary layers of the solutions. Numerical results are presented to show the utility of the method.

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Published

2019-10-09

Issue

Vol. 9 No. 4 (2019)

Section

Articles