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Abstract
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In this talk, we consider an adaptive meshing scheme for the convection-diffusion equations with mixed boundary conditions. The mesh refinement and optimization process is based on an algorithm that combines the so-call conforming centroidal Voronoi Delaunay triangulations and a residual type a posteriori error estimator for the finite volume (co-volume) discretization. Various numerical experiments including convection-dominated cases are presented and our adaptive scheme is shown to be optimal in the following sense: errors are very well equidistributed over the triangles; at all levels of refinement, the triangles remain very well shaped; and the convergence rates achieved are the best obtainable using the finite volume method.
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