Volume 16, Issue 1
Partition of unity for a class of nonlinear parabolic equation on overlapping non-matching grids

Q. Wang, K. Deng, Z. Xiong & Y. Huang

Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 16 (2007), pp. 1-13

Published online: 2007-02

Export citation
  • Abstract
A class of nonlinear parabolic equation on a polygonal domain $\Omega\subset \mathbb R^2$ is investigated in this paper. We introduce a finite element method on overlapping non-matching grids for the nonlinear parabolic equation based on the partition of unity method. We give the construction and convergence analysis for the semi-discrete and the fully discrete finite element methods. Moreover, we prove that the error of the discrete variational problem has good approximation properties. Our results are valid for any spatial dimensions. A numerical example to illustrate the theoretical results is also given.
  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{NM-16-1, author = { Q. Wang, K. Deng, Z. Xiong and Y. Huang}, title = {Partition of unity for a class of nonlinear parabolic equation on overlapping non-matching grids}, journal = {Numerical Mathematics, a Journal of Chinese Universities}, year = {2007}, volume = {16}, number = {1}, pages = {1--13}, abstract = { A class of nonlinear parabolic equation on a polygonal domain $\Omega\subset \mathbb R^2$ is investigated in this paper. We introduce a finite element method on overlapping non-matching grids for the nonlinear parabolic equation based on the partition of unity method. We give the construction and convergence analysis for the semi-discrete and the fully discrete finite element methods. Moreover, we prove that the error of the discrete variational problem has good approximation properties. Our results are valid for any spatial dimensions. A numerical example to illustrate the theoretical results is also given.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nm/8045.html} }
TY - JOUR T1 - Partition of unity for a class of nonlinear parabolic equation on overlapping non-matching grids AU - Q. Wang, K. Deng, Z. Xiong & Y. Huang JO - Numerical Mathematics, a Journal of Chinese Universities VL - 1 SP - 1 EP - 13 PY - 2007 DA - 2007/02 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nm/8045.html KW - AB - A class of nonlinear parabolic equation on a polygonal domain $\Omega\subset \mathbb R^2$ is investigated in this paper. We introduce a finite element method on overlapping non-matching grids for the nonlinear parabolic equation based on the partition of unity method. We give the construction and convergence analysis for the semi-discrete and the fully discrete finite element methods. Moreover, we prove that the error of the discrete variational problem has good approximation properties. Our results are valid for any spatial dimensions. A numerical example to illustrate the theoretical results is also given.
Q. Wang, K. Deng, Z. Xiong & Y. Huang. (1970). Partition of unity for a class of nonlinear parabolic equation on overlapping non-matching grids. Numerical Mathematics, a Journal of Chinese Universities. 16 (1). 1-13. doi:
Copy to clipboard
The citation has been copied to your clipboard