A mixed finite volume element method based on rectangular mesh for biharmonic equations

Authors:
Tongke Wang
Affiliations:
College of Mathematical Science, Tianjin Normal University, Tianjin 300074, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

Citing 7
Cited 3

On the accuracy of the finite volume element method for diffusion equations on composite grids

SIAM Journal on Numerical Analysis
Convergence of finite volume schemes for Poisson's equation on nonuniform meshes

SIAM Journal on Numerical Analysis
The node-centred finite volume approach: bridge between finite differences and finite elements

Computer Methods in Applied Mechanics and Engineering
On the Finite Volume Element Method for General Self-Adjoint Elliptic Problems

SIAM Journal on Numerical Analysis
Analysis of the cell-centred finite volume method for the diffusion equation

Journal of Computational Physics
Some mixed finite element methods for biharmonic equation

Journal of Computational and Applied Mathematics
Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems

A Rectangular Finite Volume Element Method for a Semilinear Elliptic Equation

Journal of Scientific Computing
Cubic superconvergent finite volume element method for one-dimensional elliptic and parabolic equations

Journal of Computational and Applied Mathematics
Superconvergent biquadratic finite volume element method for two-dimensional Poisson's equations

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

This paper presents a mixed finite volume element scheme based on rectangular partition for solving biharmonic equations. It also gives a kind of adaptive Uzawa iteration method for the scheme. It is rigorously proved that the scheme has first-order accuracy in H1 semi-norm and L2 norm according to the characteristics of the scheme. Finally, two numerical examples illustrate the effectiveness of the method.