Discretization on non-orthogonal, quadrilateral grids for inhomogeneous, anisotropic media
Journal of Computational Physics
A local support-operators diffusion discretization scheme for quadrilateral r-z meshes
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals
SIAM Journal on Numerical Analysis
Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
SIAM Journal on Numerical Analysis
A mortar mimetic finite difference method on non-matching grids
Numerische Mathematik
Robust convergence of multi point flux approximation on rough grids
Numerische Mathematik
A cell-centered diffusion scheme on two-dimensional unstructured meshes
Journal of Computational Physics
Enriched multi-point flux approximation for general grids
Journal of Computational Physics
A Nine Point Scheme for the Approximation of Diffusion Operators on Distorted Quadrilateral Meshes
SIAM Journal on Scientific Computing
Finite Volume Method for 2D Linear and Nonlinear Elliptic Problems with Discontinuities
SIAM Journal on Numerical Analysis
An efficient cell-centered diffusion scheme for quadrilateral grids
Journal of Computational Physics
Local flux mimetic finite difference methods
Numerische Mathematik
Journal of Computational Physics
Linearity preserving nine-point schemes for diffusion equation on distorted quadrilateral meshes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
We are interested in a robust and accurate finite volume scheme for 2-D parabolic problems derived from the cell functional minimization approach. The scheme has a local stencil, is locally conservative, treats discontinuity rigorously and leads to a symmetric positive definite linear system. Since the scheme has both cell centered unknowns and cell edge unknowns, the computational cost is an issue and a parallel algorithm is then suggested based on nonoverlapping domain decomposition approach. The interface condition is of the Dirichlet-Robin type and has a parameter @l. By choosing this parameter properly, the convergence of the iteration process could be sped up. Numerical results for linear and nonlinear problems demonstrate the good performance of the cell functional minimization scheme and its parallel version on distorted meshes.