About Uniqueness for Nonlinear Boundary Value Problems.
Adaptive finite element methods for elliptic problems: Abstract framework and applications
We consider a general abstract framework of a continuous elliptic problem set on a Hilbert space V that is approximated by a family of (discrete) problems set on a finite-dimensional space of finite dimension not necessarily included into V. We give a series of realistic conditions on an error estimator that allows to conclude that the marking strategy of bulk type leads to the geometric convergence of the adaptive algorithm. These conditions are then verified for different concrete problems...
Adaptive mixed hybrid and macro-hybrid finite element methods.
Adaptivity and variational stabilization for convection-diffusion equations
In this paper we propose and analyze stable variational formulations for convection diffusion problems starting from concepts introduced by Sangalli. We derive efficient and reliable a posteriori error estimators that are based on these formulations. The analysis of resulting adaptive solution concepts, when specialized to the setting suggested by Sangalli’s work, reveals partly unexpected phenomena related to the specific nature of the norms induced by the variational formulation. Several remedies,...
Adaptivity and variational stabilization for convection-diffusion equations∗
In this paper we propose and analyze stable variational formulations for convection diffusion problems starting from concepts introduced by Sangalli. We derive efficient and reliable a posteriori error estimators that are based on these formulations. The analysis of resulting adaptive solution concepts, when specialized to the setting suggested by Sangalli’s work, reveals partly unexpected phenomena related to the specific nature of the norms induced by the variational formulation. Several remedies,...
Addendum to the paper “Numerical solution of second-order equations on plane domains”
Advancing analysis capabilities in ANSYS through solver technology.
Alcuni risultati di teoria spettrale per l'operatore di Laplace in regioni non limitate con frontiera non regolare
Algebraic Multi Level Preconditioning Methods. I.
Alternative de Fredholm relative au problème de Dirichlet dans un polyèdre
An alternating direction implicit method for orthogonal spline collocation linear systems.
An analysis of the cell vertex method
An application of the method of spectral functions to the problem of scattering by two wedges.
An Asymptotic Finite Element Method for Improvement of Solutions of Boundary Layer Problems.
An Elliptic Boundary Value problem occurring in Magnetohydrodynamcis.
An elliptic problem with critical exponent and positive Hardy potential.
An equilibrated residual method with a computable error approximation for a singularly perturbed reaction-diffusion problem on anisotropic finite element meshes
Singularly perturbed reaction-diffusion problems exhibit in general solutions with anisotropic features, e.g. strong boundary and/or interior layers. This anisotropy is reflected in a discretization by using meshes with anisotropic elements. The quality of the numerical solution rests on the robustness of the a posteriori error estimator with respect to both, the perturbation parameters of the problem and the anisotropy of the mesh. The equilibrated residual method has been shown to provide one...
An existence and localization theorem for the solutions of a Dirichlet problem
We establish an existence theorem for a Dirichlet problem with homogeneous boundary conditions by using a general variational principle of Ricceri.
An existence result for a semipositone problem with a sign changing weight.
An existence result for nonlinear elliptic problems involving critical Sobolev exponent