The accuracy of cell vertex finite volume methods on quadrilateral meshes

Author:
Endre Süli

Journal:
Math. Comp. **59** (1992), 359-382

MSC:
Primary 65N30; Secondary 65N15, 65N50

DOI:
https://doi.org/10.1090/S0025-5718-1992-1134740-X

MathSciNet review:
1134740

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Abstract: For linear first-order hyperbolic equations in two dimensions we restate the cell vertex finite volume scheme as a finite element method. On structured meshes consisting of distorted quadrilaterals, the global error is shown to be of second order in various mesh-dependent norms, provided that the quadrilaterals are close to parallelograms in the sense that the distance between the midpoints of the diagonals is of the same order as the measure of the quadrilateral. On tensor product nonuniform meshes, the cell vertex scheme coincides with the familiar box scheme. In this case, second-order accuracy is shown without any additional assumption on the regularity of the mesh, which explains the insensitivity of the cell vertex scheme to mesh stretching in the coordinate directions, observed in practice.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1992-1134740-X

Keywords:
Finite volume methods,
stability,
error estimates

Article copyright:
© Copyright 1992
American Mathematical Society