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

Yang, Min

ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 6, pp. 1053-1067.

In this paper, by use of affine 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.

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