Convergence analysis of the rotated element on anisotropic rectangular meshes.
Convergence and Comparison Analysis of Some Numerical Schwarz Methods.
Convergence and regularization results for optimal control problems with sparsity functional
Optimization problems with convex but non-smooth cost functional subject to an elliptic partial differential equation are considered. The non-smoothness arises from a L1-norm in the objective functional. The problem is regularized to permit the use of the semi-smooth Newton method. Error estimates with respect to the regularization parameter are provided. Moreover, finite element approximations are studied. A-priori as well as a-posteriori error estimates are developed and confirmed by numerical...
Convergence and regularization results for optimal control problems with sparsity functional
Optimization problems with convex but non-smooth cost functional subject to an elliptic partial differential equation are considered. The non-smoothness arises from a L1-norm in the objective functional. The problem is regularized to permit the use of the semi-smooth Newton method. Error estimates with respect to the regularization parameter are provided. Moreover, finite element approximations are studied. A-priori as well as a-posteriori error estimates are developed and confirmed by numerical...
Convergence of a finite difference scheme for the third boundary-value problem.
Convergence of the Nonconforming Wilson Element for Arbitrary Quadrilateral Meshes.
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.
De Giorgi’s Theorem, for a Class of Strongly Degenerate Elliptic Equations
In questa Nota enunciamo, per una classe di equazioni ellittiche del secondo ordine «fortemente degeneri» a coefficienti misurabili, un teorema di hölderianità delle soluzioni deboli che estende il ben noto risultato di De Giorgi e Nash. Tale risuJtato discende dalle proprietà geometriche di opportune famiglie di sfere associate agli operatori.
Dependence of fractional powers of elliptic operators on boundary conditions
The realization of an elliptic operator A under suitable boundary conditions is considered and the dependence of the square-root of A from the various conditions is studied.