Volume 28, Issue 1
Superconvergence of Gradient Recovery Schemes on Graded Meshes for Corner Singularities

Long Chen & Hengguang Li

J. Comp. Math., 28 (2010), pp. 11-31.

Published online: 2010-02

Preview Full PDF 531 2330
Export citation
  • Abstract

For the linear finite element solution to the Poisson equation, we show that superconvergence exists for a type of graded meshes for corner singularities in polygonal domains. In particular, we prove that the L^(2)-projection from the piecewise constant field to the continuous and piecewise linear finite element space gives a better approximation in the H^(1)-norm. In contrast to the existing superconvergence results, we do not assume high regularity of the exact solution.

  • Keywords

Superconvergence Graded meshes Weighted Sobolev spaces Singular solutions The finite element method Gradient recovery schemes

  • AMS Subject Headings

65N12 65N30 65N50.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JCM-28-11, author = {}, title = {Superconvergence of Gradient Recovery Schemes on Graded Meshes for Corner Singularities}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {1}, pages = {11--31}, abstract = { For the linear finite element solution to the Poisson equation, we show that superconvergence exists for a type of graded meshes for corner singularities in polygonal domains. In particular, we prove that the L^(2)-projection from the piecewise constant field to the continuous and piecewise linear finite element space gives a better approximation in the H^(1)-norm. In contrast to the existing superconvergence results, we do not assume high regularity of the exact solution. }, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.09-m1002}, url = {http://global-sci.org/intro/article_detail/jcm/8504.html} }
TY - JOUR T1 - Superconvergence of Gradient Recovery Schemes on Graded Meshes for Corner Singularities JO - Journal of Computational Mathematics VL - 1 SP - 11 EP - 31 PY - 2010 DA - 2010/02 SN - 28 DO - http://doi.org/10.4208/jcm.2009.09-m1002 UR - https://global-sci.org/intro/article_detail/jcm/8504.html KW - Superconvergence KW - Graded meshes KW - Weighted Sobolev spaces KW - Singular solutions KW - The finite element method KW - Gradient recovery schemes AB - For the linear finite element solution to the Poisson equation, we show that superconvergence exists for a type of graded meshes for corner singularities in polygonal domains. In particular, we prove that the L^(2)-projection from the piecewise constant field to the continuous and piecewise linear finite element space gives a better approximation in the H^(1)-norm. In contrast to the existing superconvergence results, we do not assume high regularity of the exact solution.
Long Chen & Hengguang Li. (2019). Superconvergence of Gradient Recovery Schemes on Graded Meshes for Corner Singularities. Journal of Computational Mathematics. 28 (1). 11-31. doi:10.4208/jcm.2009.09-m1002
Copy to clipboard
The citation has been copied to your clipboard