On the Accuracy of the Finite Volume Element Method for Diffusion Equations on Composite Grids

This paper develops the finite volume element (FVE) method, which is similar to the so-called control volume finite element method but tailored to composite grid applications. FVE is described for the general two-dimensional diffusion equation in divergence form; O(h3/2) discretization error estimat...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 1990-06, Vol.27 (3), p.636-655
Main Authors: Cai, Zhiqiang, McCormick, Steve
Format: Article
Language:English
Subjects:
Accuracy
Approximation
Computational mathematics
Ellipticity
Error rates
Finite element analysis
Finite element method
Finite volume method
Interfaces
Linear polynomials
Mathematical constants
Mathematical functions
Mathematical notation
Partial differential equations
Stencils
Volume
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Summary:This paper develops the finite volume element (FVE) method, which is similar to the so-called control volume finite element method but tailored to composite grid applications. FVE is described for the general two-dimensional diffusion equation in divergence form; O(h3/2) discretization error estimates are then developed for the case of triangular elements. These results are improved to O(h2) using a special modification involving rectilinear elements at the grid interface.
ISSN:0036-1429
1095-7170
DOI:10.1137/0727039