A finite volume scheme is discussed for discretizing diffusion operators. Both cell-center unknowns and cell-vertex unknowns are used originally in the construction of the finite volume scheme. Then cell-vertex unknowns are eliminated by expressing them locally as linear combinations of cell-center unknowns, which is derived by the following process. First we construct a special control-volume ...

The fully nonlinear and weakly dispersive Green-Naghdi model for shallow water waves of large amplitude is studied. The original model is first recast under a new formulation more suitable for numerical resolution. An hybrid finite volume and finite difference splitting approach is then proposed. The hyperbolic part of the equations is handled with a high-order finite volume scheme allowing for...

A stable hybrid method for hyperbolic problems that combines the unstructured finite volume method with high-order finite difference methods has been developed. The coupling procedure is based on energy estimates and stability can be guaranteed. Numerical calculations verify that the hybrid method is efficient and accurate.

1. GENERAL FORM OF FINITE VOLUME METHODS We consider vertex-centered finite volume methods for solving diffusion type elliptic equation (1) −∇ · (K∇u) = f in Ω, with suitable Dirichlet or Neumann boundary conditions. Here Ω ⊂ R is a polyhedral domain (d ≥ 2), the diffusion coefficient K(x) is a d× d symmetric matrix function that is uniformly positive definite on Ω with components in L∞(Ω), and...

Computational modelling has received significant attention in the research community over the past few decades due to its pronounced contribution in better understanding of the nature, as well as in the development of advanced technologies. The modelling of more and more complex transport physical systems helps the community to address important issues, like identification of environmental prob...

1. Lax equivalence theorem 1 2. Abstract error analysis 2 3. Application: Finite difference method 3 4. Application: Finite element method 4 5. Application: Conforming Discretization of Variational Problems 5 6. Application: Perturbed Discretization 6 7. Application: Nonconforming finite element methods 7 8. Application: Finite volume method 7 9. Application: Superconvergence of linear finite e...