Some errors estimates for the box method
SIAM Journal on Numerical Analysis
Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
Convergence of finite volume schemes for Poisson's equation on nonuniform meshes
SIAM Journal on Numerical Analysis
Mixed Covolume Methods for Elliptic Problems on Triangular Grids
SIAM Journal on Numerical Analysis
A general mixed covolume framework for constructing conservative schemes for elliptic problems
Mathematics of Computation
Superconvergence of Mixed Finite Element Approximations over Quadrilaterals
SIAM Journal on Numerical Analysis
On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials
SIAM Journal on Numerical Analysis
Analysis of linear and quadratic simplicial finite volume methods for elliptic equations
Numerische Mathematik
L2 error estimates and superconvergence of the finite volume element methods on quadrilateral meshes
Advances in Computational Mathematics
Higher-order finite volume methods for elliptic boundary value problems
Advances in Computational Mathematics
L2 error estimates and superconvergence of the finite volume element methods on quadrilateral meshes
Advances in Computational Mathematics
On the semi-discrete stabilized finite volume method for the transient Navier---Stokes equations
Advances in Computational Mathematics
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This paper is concerned with the finite volume element methods on quadrilateral mesh for second-order elliptic equation with variable coefficients. An error estimate in L 2 norm is shown on the quadrilateral meshes consisting of h 2-parallelograms. Superconvergence of numerical solution is also derived in an average gradient norm on h 2-uniform quadrilateral meshes. Numerical examples confirm our theoretical conclusions.