Journal of Computational Physics
Monotone finite volume schemes for diffusion equations on polygonal meshes
Journal of Computational Physics
Numerical solutions of Euler--Poisson systems for potential flows
Applied Numerical Mathematics
The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes
Journal of Computational Physics
The finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes
Journal of Computational Physics
The Discrete Duality Finite Volume Method for Convection-diffusion Problems
SIAM Journal on Numerical Analysis
Error Analysis for a Mimetic Discretization of the Steady Stokes Problem on Polyhedral Meshes
SIAM Journal on Numerical Analysis
A Mimetic Discretization of the Stokes Problem with Selected Edge Bubbles
SIAM Journal on Scientific Computing
Construction and Convergence Study of Schemes Preserving the Elliptic Local Maximum Principle
SIAM Journal on Numerical Analysis
A 3D Discrete Duality Finite Volume Method for Nonlinear Elliptic Equations
SIAM Journal on Scientific Computing
An improved monotone finite volume scheme for diffusion equation on polygonal meshes
Journal of Computational Physics
Mathematics and Computers in Simulation
SIAM Journal on Numerical Analysis
Mimetic finite difference method
Journal of Computational Physics
A Family of Finite Volume Schemes of Arbitrary Order on Rectangular Meshes
Journal of Scientific Computing
Hi-index | 0.03 |
We present a new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which simultaneously gives an approximation of the solution and of its gradient. The approximate solution is shown to converge to the continuous one as the size of the mesh tends to 0, and an error estimate is given. An easy implementation method is then proposed, and the efficiency of the scheme is shown on various types of grids and for various diffusion matrices.