Convergence rate estimate for a domain decomposition method.
Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
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...
Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes
Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes
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...
Convexity estimates for nonlinear elliptic equations and application to free boundary problems
Convexity of level sets for solutions to nonlinear elliptic problems in convex rings.
Costruzione di spike-layers multidimensionali
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.
Counter-Examples to Boundary Estimates for Two-Dimensional Elliptic Systems.
Crack detection by the topological gradient method
Critical Neumann problem with competing Hardy potentials.
Critical point theory for nonsmooth energy functionals and applications.