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Volume 43, Issue 1
Adaptive Virtual Element Method for Convection Dominated Diffusion Equations

Qiming Wang & Zhaojie Zhou

DOI: 10.4208/jcm.2309-m2021-0366

J. Comp. Math., 43 (2025), pp. 174-202.

Published online: 2024-11

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  • Abstract

In this paper, a robust residual-based a posteriori estimate is discussed for the Streamline Upwind/Petrov Galerkin (SUPG) virtual element method (VEM) discretization of convection dominated diffusion equation. A global upper bound and a local lower bound for the a posteriori error estimates are derived in the natural SUPG norm, where the global upper estimate relies on some hypotheses about the interpolation errors and SUPG virtual element discretization errors. Based on the Dörfler’s marking strategy, adaptive VEM algorithm drived by the error estimators is used to solve the problem on general polygonal meshes. Numerical experiments show the robustness of the a posteriori error estimates.

  • Keywords

A posteriori estimate, SUPG virtual element method, Convection dominated diffusion equation, Adaptive VEM algorithm.

  • AMS Subject Headings

65N15, 65N30, 65N50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-43-174, author = {Wang , Qiming and Zhou , Zhaojie}, title = {Adaptive Virtual Element Method for Convection Dominated Diffusion Equations}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {43}, number = {1}, pages = {174--202}, abstract = {

In this paper, a robust residual-based a posteriori estimate is discussed for the Streamline Upwind/Petrov Galerkin (SUPG) virtual element method (VEM) discretization of convection dominated diffusion equation. A global upper bound and a local lower bound for the a posteriori error estimates are derived in the natural SUPG norm, where the global upper estimate relies on some hypotheses about the interpolation errors and SUPG virtual element discretization errors. Based on the Dörfler’s marking strategy, adaptive VEM algorithm drived by the error estimators is used to solve the problem on general polygonal meshes. Numerical experiments show the robustness of the a posteriori error estimates.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2309-m2021-0366}, url = {http://global-sci.org/intro/article_detail/jcm/23534.html} }
TY - JOUR T1 - Adaptive Virtual Element Method for Convection Dominated Diffusion Equations AU - Wang , Qiming AU - Zhou , Zhaojie JO - Journal of Computational Mathematics VL - 1 SP - 174 EP - 202 PY - 2024 DA - 2024/11 SN - 43 DO - http://doi.org/10.4208/jcm.2309-m2021-0366 UR - https://global-sci.org/intro/article_detail/jcm/23534.html KW - A posteriori estimate, SUPG virtual element method, Convection dominated diffusion equation, Adaptive VEM algorithm. AB -

In this paper, a robust residual-based a posteriori estimate is discussed for the Streamline Upwind/Petrov Galerkin (SUPG) virtual element method (VEM) discretization of convection dominated diffusion equation. A global upper bound and a local lower bound for the a posteriori error estimates are derived in the natural SUPG norm, where the global upper estimate relies on some hypotheses about the interpolation errors and SUPG virtual element discretization errors. Based on the Dörfler’s marking strategy, adaptive VEM algorithm drived by the error estimators is used to solve the problem on general polygonal meshes. Numerical experiments show the robustness of the a posteriori error estimates.

Wang , Qiming and Zhou , Zhaojie. (2024). Adaptive Virtual Element Method for Convection Dominated Diffusion Equations. Journal of Computational Mathematics. 43 (1). 174-202. doi:10.4208/jcm.2309-m2021-0366
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