48 citations · 116 across the 10 of their papers we have counts for
13 papers
A~posteriori error analysis for optimization with PDE constraints
Fernando Gaspoz, Christian Kreuzer, Andreas Veeser +1
We consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing up…
Strictly equivalent a~posteriori error estimators for quasi-optimal nonconforming methods
Christian Kreuzer, Matthias Rott, Andreas Veeser +1
We devise a posteriori error estimators for quasi-optimal nonconforming finite element methods approximating symmetric elliptic problems of second and fourth order. These estimator…
Adaptive Finite Element Methods
Andrea Bonito, Claudio Canuto, Ricardo H. Nochetto +1
This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment i…
A Nodally Bound-Preserving Finite Element Method
Gabriel Barrenechea, Emmanuil Georgoulis, Tristan Pryer +1
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator…
Near-best adaptive approximation on conforming meshes
Peter Binev, Francesca Fierro, Andreas Veeser
We devise a generalization of tree approximation that generates conforming meshes, i.e., meshes with a particular structure like edge-to-edge triangulations. A key feature of this…
Quasi-best approximation in optimization with PDE constraints
Fernando Gaspoz, Christian Kreuzer, Andreas Veeser +1
We consider finite element solutions to quadratic optimization problems, where the state depends on the control via a well-posed linear partial differential equation. Exploiting th…
Oscillation in a posteriori error estimation
Christian Kreuzer, Andreas Veeser
In a posteriori error analysis, the relationship between error and estimator is usually spoiled by so-called oscillation terms, which cannot be bounded by the error. In order to re…
Quasi-optimal nonconforming methods for symmetric elliptic problems. III -- DG and other interior penalty methods
Andreas Veeser, Pietro Zanotti
We devise new variants of the following nonconforming finite element methods: DG methods of fixed arbitrary order for the Poisson problem, the Crouzeix-Raviart interior penalty met…
Quasi-optimal nonconforming methods for symmetric elliptic problems. II -- Overconsistency and classical nonconforming elements
Andreas Veeser, Pietro Zanotti
We devise variants of classical nonconforming methods for symmetric elliptic problems. These variants differ from the original ones only by transforming discrete test functions int…
Quasi-optimal nonconforming methods for symmetric elliptic problems. I -- Abstract theory
Andreas Veeser, Pietro Zanotti
We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optim…
A posteriori error estimates with point sources in fractional Sobolev spaces
Fernando D. Gaspoz, Pedro Morin, Andreas Veeser
We consider Poisson's equation with a finite number of weighted Dirac masses as a source term, together with its discretization by means of conforming finite elements. For the erro…
Robust Localization of the Best Error with Finite Elements in the Reaction-Diffusion Norm
Francesca Tantardini, Andreas Veeser, R"udiger Verf"urth
We consider the approximation in the reaction-diffusion norm with continuous finite elements and prove that the best error is equivalent to a sum of the local best errors on pairs…
Approximating gradients with continuous piecewise polynomial functions
Andreas Veeser
Motivated by conforming finite element methods for elliptic problems of second order, we analyze the approximation of the gradient of a target function by continuous piecewise poly…