Volume 24, Issue 1
P1-Nonconforming Quadrilateral Finite Volume Element Method and Its Cascadic Multigrid Algorithm

Hong-ying Man & Zhong-ci Shi

DOI:

J. Comp. Math., 24 (2006), pp. 59-80

Published online: 2006-02

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  • Abstract

In this paper, we discuss the finite volume element method of $P_1$-nonconforming quadrilateral element for elliptic problems and obtain optimal error estimates for general quadrilateral partition. An optimal cascadic multigrid algorithm is proposed to solve the nonsymmetric large-scale system resulting from such discretization. Numerical experiments are reported to support our theoretical results.

  • Keywords

Finite volume element method cascadic multigrid elliptic problems

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@Article{JCM-24-59, author = {}, title = {P1-Nonconforming Quadrilateral Finite Volume Element Method and Its Cascadic Multigrid Algorithm}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {1}, pages = {59--80}, abstract = { In this paper, we discuss the finite volume element method of $P_1$-nonconforming quadrilateral element for elliptic problems and obtain optimal error estimates for general quadrilateral partition. An optimal cascadic multigrid algorithm is proposed to solve the nonsymmetric large-scale system resulting from such discretization. Numerical experiments are reported to support our theoretical results. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8734.html} }
TY - JOUR T1 - P1-Nonconforming Quadrilateral Finite Volume Element Method and Its Cascadic Multigrid Algorithm JO - Journal of Computational Mathematics VL - 1 SP - 59 EP - 80 PY - 2006 DA - 2006/02 SN - 24 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8734.html KW - Finite volume element method KW - cascadic multigrid KW - elliptic problems AB - In this paper, we discuss the finite volume element method of $P_1$-nonconforming quadrilateral element for elliptic problems and obtain optimal error estimates for general quadrilateral partition. An optimal cascadic multigrid algorithm is proposed to solve the nonsymmetric large-scale system resulting from such discretization. Numerical experiments are reported to support our theoretical results.
Hong-ying Man & Zhong-ci Shi. (1970). P1-Nonconforming Quadrilateral Finite Volume Element Method and Its Cascadic Multigrid Algorithm. Journal of Computational Mathematics. 24 (1). 59-80. doi:
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