$P_1$-Nonconforming Quadrilateral Finite Volume Element Method and Its Cascadic Multigrid Algorithm for Elliptic Problems
Year: 2006
Author: Hongying Man, Zhongci Shi
Journal of Computational Mathematics, Vol. 24 (2006), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2006-JCM-8734
Journal of Computational Mathematics, Vol. 24 (2006), Iss. 1 : pp. 59–80
Published online: 2006-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Finite volume element method cascadic multigrid elliptic problems.