@Article{JCM-24-59, author = {Man , Hongying and Shi , Zhongci}, 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} }