A parallel adaptive finite volume method for nanoscale double-gate MOSFETs simulation
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
A parallel adaptive finite volume method for nanoscale double-gate MOSFETs simulation
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
Error estimates for the finite volume discretization for the porous medium equation
Journal of Computational and Applied Mathematics
A numerical method for mass conservative coupling between fluid flow and solute transport
Applied Numerical Mathematics
Discrete Sobolev-Poincaré Inequalities for Voronoi Finite Volume Approximations
SIAM Journal on Numerical Analysis
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We study here the convergence of a finite volume scheme for a diffusion convection equation on an open bounded set of $\R^\dim$ ($\dim=2$ or $3$) for which we consider Dirichlet, Neumann, or Robin boundary conditions. We consider unstructured meshes which include Voronoi or triangular meshes; we use for the diffusion term an "s points" (where s is the number of sides of each cell) finite volume scheme and for the convection term an upstream finite volume scheme. Assuming the exact solution at least in H2 we prove error estimates in a discrete $H^1_0$ norm of order the size of the mesh. Discrete Poincaré inequalities then allow one to prove error estimates in the L2 norm.