A second-order finite volume element method on quadrilateral meshes for elliptic equations

摘要

In this paper, by use of a. ne biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in H-1-norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method.