Loading [MathJax]/jax/output/HTML-CSS/config.js
full
search.png

Search

close.png

Cancel

arrow
Volume 15, Issue 1
A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations

Guanrong Li, Yanping Chen & Yunqing Huang

DOI: 10.4208/nmtma.OA-2020-0165

Numer. Math. Theor. Meth. Appl., 15 (2022), pp. 68-90.

Published online: 2022-02

Preview Full PDF 3456 39714

Cited by

google scholar semantic scholar
Export citation
  • Abstract

In this paper, a robust modified weak Galerkin (MWG) finite element method for reaction-diffusion equations is proposed and investigated. An advantage of this method is that it can deal with the singularly perturbed reaction-diffusion equations. Another advantage of this method is that it produces fewer degrees of freedom than the traditional WG method by eliminating the element boundaries freedom. It is worth pointing out that, in our method, the test functions space is the same as the finite element space, which is helpful for the error analysis. Optimal-order error estimates are established for the corresponding numerical approximation in various norms. Some numerical results are reported to confirm the theory.

  • Keywords

Reaction-diffusion equations, singular perturbation, modified weak Galerkin, finite element methods, discrete gradient.

  • AMS Subject Headings

Primary: 65N15, 65N30；Secondary: 35J50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{NMTMA-15-68, author = {Li , GuanrongChen , Yanping and Huang , Yunqing}, title = {A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2022}, volume = {15}, number = {1}, pages = {68--90}, abstract = {

In this paper, a robust modified weak Galerkin (MWG) finite element method for reaction-diffusion equations is proposed and investigated. An advantage of this method is that it can deal with the singularly perturbed reaction-diffusion equations. Another advantage of this method is that it produces fewer degrees of freedom than the traditional WG method by eliminating the element boundaries freedom. It is worth pointing out that, in our method, the test functions space is the same as the finite element space, which is helpful for the error analysis. Optimal-order error estimates are established for the corresponding numerical approximation in various norms. Some numerical results are reported to confirm the theory.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2020-0165}, url = {http://global-sci.org/intro/article_detail/nmtma/20221.html} }
TY - JOUR T1 - A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations AU - Li , Guanrong AU - Chen , Yanping AU - Huang , Yunqing JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 68 EP - 90 PY - 2022 DA - 2022/02 SN - 15 DO - http://doi.org/10.4208/nmtma.OA-2020-0165 UR - https://global-sci.org/intro/article_detail/nmtma/20221.html KW - Reaction-diffusion equations, singular perturbation, modified weak Galerkin, finite element methods, discrete gradient. AB -

In this paper, a robust modified weak Galerkin (MWG) finite element method for reaction-diffusion equations is proposed and investigated. An advantage of this method is that it can deal with the singularly perturbed reaction-diffusion equations. Another advantage of this method is that it produces fewer degrees of freedom than the traditional WG method by eliminating the element boundaries freedom. It is worth pointing out that, in our method, the test functions space is the same as the finite element space, which is helpful for the error analysis. Optimal-order error estimates are established for the corresponding numerical approximation in various norms. Some numerical results are reported to confirm the theory.

Li , GuanrongChen , Yanping and Huang , Yunqing. (2022). A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations. Numerical Mathematics: Theory, Methods and Applications. 15 (1). 68-90. doi:10.4208/nmtma.OA-2020-0165
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard