Volume 24, Issue 1
$P_1$-Nonconforming Quadrilateral Finite Volume Element Method and Its Cascadic Multigrid Algorithm for Elliptic Problems

Hongying Man Zhongci Shi

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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COPYRIGHT: © Global Science Press

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@Article{JCM-24-59, author = {Hongying Man , and Zhongci Shi , }, title = {$P_1$-Nonconforming Quadrilateral Finite Volume Element Method and Its Cascadic Multigrid Algorithm for Elliptic Problems}, 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 - $P_1$-Nonconforming Quadrilateral Finite Volume Element Method and Its Cascadic Multigrid Algorithm for Elliptic Problems AU - Hongying Man , AU - Zhongci Shi , 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, cascadic multigrid, 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.

Hongying Man & Zhongci Shi. (1970). $P_1$-Nonconforming Quadrilateral Finite Volume Element Method and Its Cascadic Multigrid Algorithm for Elliptic Problems. Journal of Computational Mathematics. 24 (1). 59-80. doi:
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