Geodesic
A second-order finite volume element method on quadrilateral meshes for elliptic equations
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 6, pp. 1053-1067

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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.

DOI : 10.1051/m2an:2007002
Classification : 65N30, 65N15
Keywords: finite volume element, second-order, quadrilateral meshes, error estimates 
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     title = {A second-order finite volume element method on quadrilateral meshes for elliptic equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1053--1067},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {6},
     year = {2006},
     doi = {10.1051/m2an:2007002},
     mrnumber = {2297104},
     zbl = {1141.65081},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007002/}
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Yang, Min. A second-order finite volume element method on quadrilateral meshes for elliptic equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 6, pp. 1053-1067. doi: 10.1051/m2an:2007002

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