P1-Nonconforming Quadrilateral Finite Volume Methods for the Semilinear Elliptic Equations

In this paper we use P1-nonconforming quadrilateral finite volume methods with interpolated coefficients to solve the semilinear elliptic problems. Two types of control volumes are applied. Optimal error estimates in H1-norm on the quadrilateral mesh and superconvergence of derivative on the rectangular mesh are derived by using the continuity argument, respectively. In addition, numerical experiments are presented adequately to confirm the theoretical analysis and optimal error estimates in L2-norm is also observed obviously. Compared with the standard Q1-conforming quadrilateral element, numerical results of the proposed finite volume methods show its better performance than others.

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