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Volume 17, Issue 2
An Error Estimate of a Eulerian-Lagrangian Localized Adjoint Method for a Space-Fractional Advection Diffusion Equation

Tingting Wang, Xiaofan Li & Hong Wang

Int. J. Numer. Anal. Mod., 17 (2020), pp. 151-171.

Published online: 2020-02

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  • 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.

  • Keywords

Space-fractional advection diffusion, fractional Laplacian, characteristic method, error estimate, superdiffusive transport.

  • AMS Subject Headings

35R20, 26A33, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ttwsmile@163.com (Tingting Wang)

lix@iit.edu (Xiaofan Li)

hwang@math.sc.edu (Hong Wang)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-17-151, author = {Tingting and Wang and ttwsmile@163.com and 6542 and School of Mathematics, Shandong University, Jinan 250100, Shandong, China and Tingting Wang and Xiaofan and Li and lix@iit.edu and 6541 and Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA and Xiaofan Li and Hong and Wang and hwang@math.sc.edu and 5257 and Department of Mathematics, University of South Carolina, SC, USA. and Hong Wang}, title = {An Error Estimate of a Eulerian-Lagrangian Localized Adjoint Method for a Space-Fractional Advection Diffusion Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {2}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13645.html} }
TY - JOUR T1 - An Error Estimate of a Eulerian-Lagrangian Localized Adjoint Method for a Space-Fractional Advection Diffusion Equation AU - Wang , Tingting AU - Li , Xiaofan AU - Wang , Hong JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 151 EP - 171 PY - 2020 DA - 2020/02 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13645.html KW - Space-fractional advection diffusion, fractional Laplacian, characteristic method, error estimate, superdiffusive transport. AB -

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.

Tingting Wang, Xiaofan Li & Hong Wang. (2020). An Error Estimate of a Eulerian-Lagrangian Localized Adjoint Method for a Space-Fractional Advection Diffusion Equation. International Journal of Numerical Analysis and Modeling. 17 (2). 151-171. doi:
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