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Convergence analysis of a finite volume method via a new nonconforming finite element method. (English) Zbl 0903.65084
The article is concerned with a convergence theory for a finite volume method and a nonconforming finite element method for Poisson’s equation (with Dirichlet boundary conditions) on a bounded convex polynomial domain in \(\mathbb{R}^2\). The finite volume method is formulated via Voronoi box partitions, while the finite element method uses the corresponding dual box partition. Since both methods amount to the same linear system of discretized equations, convergence results for the finite volume method can be obtained by convergence analysis of the finite element method. The latter is performed on the basis of the second lemma of Strang.
Reviewer: M.Plum (Karlsruhe)

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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