# The accuracy of cell vertex finite volume methods on quadrilateral meshes

## 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 guadrilateral. 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. 17 refs.

- Authors:

- Publication Date:

- OSTI Identifier:
- 6701472

- Resource Type:
- Journal Article

- Journal Name:
- Mathematics of Computation; (United States)

- Additional Journal Information:
- Journal Volume: 59:200; Journal ID: ISSN 0025-5718

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FINITE ELEMENT METHOD; EVALUATION; FLUID FLOW; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; ANALYTICAL SOLUTION; TWO-DIMENSIONAL CALCULATIONS; CALCULATION METHODS; DIFFERENTIAL EQUATIONS; EQUATIONS; NUMERICAL SOLUTION; 661300* - Other Aspects of Physical Science- (1992-)

### Citation Formats

```
Sueli, E.
```*The accuracy of cell vertex finite volume methods on quadrilateral meshes*. United States: N. p., 1992.
Web. doi:10.2307/2153062.

```
Sueli, E.
```*The accuracy of cell vertex finite volume methods on quadrilateral meshes*. United States. doi:10.2307/2153062.

```
Sueli, E. Thu .
"The accuracy of cell vertex finite volume methods on quadrilateral meshes". United States. doi:10.2307/2153062.
```

```
@article{osti_6701472,
```

title = {The accuracy of cell vertex finite volume methods on quadrilateral meshes},

author = {Sueli, E},

abstractNote = {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 guadrilateral. 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. 17 refs.},

doi = {10.2307/2153062},

journal = {Mathematics of Computation; (United States)},

issn = {0025-5718},

number = ,

volume = 59:200,

place = {United States},

year = {1992},

month = {10}

}