Some errors estimates for the box method
SIAM Journal on Numerical Analysis
On convergence of block-centered finite differences for elliptic-problems
SIAM Journal on Numerical Analysis
The finite volume element method for diffusion equations on general triangulations
SIAM Journal on Numerical Analysis
Finite volume methods for convection-diffusion problems
SIAM Journal on Numerical Analysis
Mixed Covolume Methods for Elliptic Problems on Triangular Grids
SIAM Journal on Numerical Analysis
Mixed Covolume Methods on Rectangular Grids For Elliptic Problems
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
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We propose in this contribution a new BVP discretization method which represents the unknown distribution as well as its derivatives by piecewise constant distributions (PCD) but on distinct meshes. Once the meshes are chosen, it is relatively straightforward to define an approximate variational formulation of the BVP on the associated PCD spaces and hence to derive the discrete equations. We end with the same scheme as the corner mesh box method and we display a precise relation between the exact solution and our approximation, which holds in the absence of absorption. We also compare these results with other approaches using a mixed variational formulation of the same BVP and sharing with our method the use of several meshes. We show that PCD approximations can also be used in this context leading, on rectangular meshes, to the same scheme as the centered box method.