An analysis of the cell vertex method. (English) Zbl 0822.65078
The authors propose an analysis of the cell vertex scheme, based on mesh- dependent norms in a nonconforming Petrov-Galerkin framework. A mapping is introduced between the trial and test spaces similar to the upwinded test functions of finite element methods or the upwinded control volumes of finite volume methods.
Particular mappings are used to analyze the one-dimensional convection- diffusion problem. For pure convection in two dimensions a new natural seminorm is used to prove local and global error estimates for the cases of flow transverse and parallel to the grid.
Particular mappings are used to analyze the one-dimensional convection- diffusion problem. For pure convection in two dimensions a new natural seminorm is used to prove local and global error estimates for the cases of flow transverse and parallel to the grid.
Reviewer: E.Krause (Aachen)
MSC:
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
Keywords:
cell vertex method; nonconforming Petrov-Galerkin method; finite element methods; finite volume methods; convection-diffusion problem; error estimatesReferences:
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