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Volume 38, Issue 6
Discontinuous Galerkin Methods and Their Adaptivity for the Tempered Fractional (Convection) Diffusion Equations

Xudong Wang & Weihua Deng

DOI: 10.4208/jcm.1906-m2019-0040

J. Comp. Math., 38 (2020), pp. 839-867.

Published online: 2020-06

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  • Abstract

This paper focuses on the adaptive discontinuous Galerkin (DG) methods for the tempered fractional (convection) diffusion equations. The DG schemes with interior penalty for the diffusion term and numerical flux for the convection term are used to solve the equations, and the detailed stability and convergence analyses are provided. Based on the derived posteriori error estimates, the local error indicator is designed. The theoretical results and the effectiveness of the adaptive DG methods are, respectively, verified and displayed by the extensive numerical experiments. The strategy of designing adaptive schemes presented in this paper works for the general PDEs with fractional operators.

  • Keywords

Adaptive DG methods, Tempered fractional equations, Posteriori error estimate.

  • AMS Subject Headings

26A33, 65M60, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xdwang14@lzu.edu.cn (Xudong Wang)

dengwh@lzu.edu.cn (Weihua Deng)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-839, author = {Wang , Xudong and Deng , Weihua}, title = {Discontinuous Galerkin Methods and Their Adaptivity for the Tempered Fractional (Convection) Diffusion Equations}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {6}, pages = {839--867}, abstract = {

This paper focuses on the adaptive discontinuous Galerkin (DG) methods for the tempered fractional (convection) diffusion equations. The DG schemes with interior penalty for the diffusion term and numerical flux for the convection term are used to solve the equations, and the detailed stability and convergence analyses are provided. Based on the derived posteriori error estimates, the local error indicator is designed. The theoretical results and the effectiveness of the adaptive DG methods are, respectively, verified and displayed by the extensive numerical experiments. The strategy of designing adaptive schemes presented in this paper works for the general PDEs with fractional operators.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1906-m2019-0040}, url = {http://global-sci.org/intro/article_detail/jcm/16970.html} }
TY - JOUR T1 - Discontinuous Galerkin Methods and Their Adaptivity for the Tempered Fractional (Convection) Diffusion Equations AU - Wang , Xudong AU - Deng , Weihua JO - Journal of Computational Mathematics VL - 6 SP - 839 EP - 867 PY - 2020 DA - 2020/06 SN - 38 DO - http://doi.org/10.4208/jcm.1906-m2019-0040 UR - https://global-sci.org/intro/article_detail/jcm/16970.html KW - Adaptive DG methods, Tempered fractional equations, Posteriori error estimate. AB -

This paper focuses on the adaptive discontinuous Galerkin (DG) methods for the tempered fractional (convection) diffusion equations. The DG schemes with interior penalty for the diffusion term and numerical flux for the convection term are used to solve the equations, and the detailed stability and convergence analyses are provided. Based on the derived posteriori error estimates, the local error indicator is designed. The theoretical results and the effectiveness of the adaptive DG methods are, respectively, verified and displayed by the extensive numerical experiments. The strategy of designing adaptive schemes presented in this paper works for the general PDEs with fractional operators.

Wang , Xudong and Deng , Weihua. (2020). Discontinuous Galerkin Methods and Their Adaptivity for the Tempered Fractional (Convection) Diffusion Equations. Journal of Computational Mathematics. 38 (6). 839-867. doi:10.4208/jcm.1906-m2019-0040
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