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Displaying 121 –
140 of
189
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...
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,...
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,...
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...
We establish an existence theorem for a Dirichlet problem with homogeneous boundary conditions by using a general variational principle of Ricceri.
Currently displaying 121 –
140 of
189