P₁-nonconforming quadrilateral finite volume element method and its cascadic multigrid algorithm for Elliptic problems

In this paper, we discuss the finite volume element method of P₁-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 non-symmetric large-scale system resulting from such discretization. Numerical experiments are reported to support our theoretical results.