P₁ -nonconforming Quadrilateral Fnite Volume Methods For The Semilinear Elliptic Equations

In this paper we consider P1-nonconforming quadrilateral finite volume methods forthe semilinear elliptic problems by using the idea of interpolated coe?cients. Two typesof dual partitions are used. Optimal convergence rate in H1-norm over the quadrilateralgrids and superconvergence of derivative over the rectangular grids are derived by usingthe continuity argument, respectively. In addition, numerical experiments to confirm thetheoretical results are presented adequately and optimal convergence rate in L2-norm arealso observed obviously. Compared with the standard Q1-conforming quadrilateral ele-ment, numerical results of the proposed finite volume schemes show its better performancethan others.