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In this paper, a class of cell centered finite volume schemes,
on general unstructured meshes, for a linear convection-diffusion
problem, is studied. The convection and the diffusion are respectively
approximated by means of an upwind scheme and the so called diamond
cell method [4]. Our main result is an error estimate of
order h, assuming only the W2,p (for p>2) regularity of the
continuous solution, on a mesh of quadrangles. The proof is based on an
extension of the ideas developed in...
We study a finite volume method, used to approximate the solution of the linear two dimensional convection diffusion equation, with mixed Dirichlet and Neumann boundary conditions, on Cartesian meshes refined by an automatic technique (which leads to meshes with hanging nodes). We propose an analysis through a discrete variational approach, in a discrete H1 finite volume space. We actually prove the convergence of the scheme in a discrete H1 norm, with an error estimate of order O(h) (on meshes...
Si studiano soluzioni positive dellequazione in , dove , ed è un piccolo parametro positivo. Si impongono in genere condizioni al bordo di Neumann. Quando tende a zero, dimostriamo esistenza di soluzioni che si concentrano su curve o varietà.
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