Hierarchical error estimates for finite volume approximation solution of elliptic equations
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Superconvergent biquadratic finite volume element method for two-dimensional Poisson's equations
Journal of Computational and Applied Mathematics
A New Class of High Order Finite Volume Methods for Second Order Elliptic Equations
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Biquadratic finite volume element methods based on optimal stress points for parabolic problems
Journal of Computational and Applied 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
A posteriori error analysis for discontinuous finite volume methods of elliptic interface problems
Journal of Computational and Applied Mathematics
A Family of Finite Volume Schemes of Arbitrary Order on Rectangular Meshes
Journal of Scientific Computing
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This paper is devoted to analysis of some convergent properties of both linear and quadratic simplicial finite volume methods (FVMs) for elliptic equations. For linear FVM on domains in any dimensions, the inf-sup condition is established in a simple fashion. It is also proved that the solution of a linear FVM is super-close to that of a relevant finite element method (FEM). As a result, some a posterior error estimates and also algebraic solvers for FEM are extended to FVM. For quadratic FVM on domains in two dimensions, the inf-sup condition is established under some weak condition on the grid.