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Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes. (English) Zbl 0972.65081
The numerical solution of the linear two-dimensional convection-diffusion equation, with mixed Dirichlet and Neumann boundary conditions, is considered. For the approximation the finite volume method on Cartesian meshes refined using an automatic technique is proposed. This technique leads to meshes with hanging nodes. An analysis through a discrete variational approach in a discrete \(H^1\) finite volume space is used. The convergence of this scheme in a discrete \(H^1\) norm, with an error estimate of order \(O(h)\), where \(h\) is the size of the mesh is proved.

65N12 Stability and convergence of numerical methods 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
65N15 Error bounds for boundary value problems involving PDEs
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