Symmetric modified finite volume element methods for self-adjoint elliptic and parabolic problems
Journal of Computational and Applied Mathematics
A symmetric finite volume scheme for selfadjoint elliptic problems
Journal of Computational and Applied Mathematics
A mixed finite volume element method based on rectangular mesh for biharmonic equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Error estimates for finite volume element methods for convection-diffusion-reaction equations
Applied Numerical Mathematics
The finite volume method based on stabilized finite element for the stationary Navier-Stokes problem
Journal of Computational and Applied Mathematics
A penalty finite volume method for the transient Navier--Stokes equations
Applied Numerical Mathematics
Mortar finite volume element method with Crouzeix--Raviart element for parabolic problems
Applied Numerical Mathematics
Error estimation of a quadratic finite volume method on right quadrangular prism grids
Journal of Computational and Applied Mathematics
The finite volume element method for the pollution in groundwater flow
Neural, Parallel & Scientific Computations
A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations
Applied Numerical Mathematics
A New Class of High Order Finite Volume Methods for Second Order Elliptic Equations
SIAM Journal on Numerical Analysis
Unified Analysis of Finite Volume Methods for the Stokes Equations
SIAM Journal on Numerical Analysis
Biquadratic finite volume element methods based on optimal stress points for parabolic problems
Journal of Computational and Applied Mathematics
Convergence of the discontinuous finite volume method for elliptic problems with minimal regularity
Journal of Computational and Applied Mathematics
Higher-order finite volume methods for elliptic boundary value problems
Advances in Computational Mathematics
Applied Numerical Mathematics
On the semi-discrete stabilized finite volume method for the transient Navier---Stokes equations
Advances in Computational Mathematics
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The finite volume element method (FVE) is a discretization technique for partial differential equations. This paper develops discretization energy error estimates for general self-adjoint elliptic boundary value problems with FVE based on triangulations, on which there exist linear finite element spaces, and a very general type of control volumes (covolumes).The energy error estimates of this paper are also optimal but the restriction conditions for the covolumes given in [R. E. Bank and D. J. Rose, SIAM J. Numer. Anal., 24 (1987), pp. 777--787], [Z. Q. Cai, Numer. Math., 58 (1991), pp. 713--735] are removed. The authors finally provide a counterexample to show that an expected L2-error estimate does not exist in the usual sense. It is conjectured that the optimal order of $\|u-u_h\|_{0,\Omega}$ should be O(h) for the general case.