Some errors estimates for the box method
SIAM Journal on Numerical Analysis
On the accuracy of the finite volume element method for diffusion equations on composite grids
SIAM Journal on Numerical Analysis
The finite volume element method for diffusion equations on general triangulations
SIAM Journal on Numerical Analysis
On the Finite Volume Element Method for General Self-Adjoint Elliptic Problems
SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Journal of Computational and Applied Mathematics
Two-grid finite volume element methods for semilinear parabolic problems
Applied Numerical Mathematics
Biquadratic finite volume element methods based on optimal stress points for parabolic problems
Journal of Computational and Applied Mathematics
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The finite volume element method is a discretization technique for partial differential equations, but in general case the coefficient matrix of its linear system is not symmetric, even for the self-adjoint continuous problem. In this paper we develop a kind of symmetric modified finite volume element methods both for general self-adjoint elliptic and for parabolic problems on general discretization, their coefficient matrix are symmetric. We give the optimal order energy norm error estimates. We also prove that the difference between the solutions of the finite volume element method and symmetric modified finite volume element method is a high order term.