Zobrazeno 1 - 10
of 122
pro vyhledávání: '"VEESER, ANDREAS"'
Publikováno v:
Acta Numerica 33 (2024) 163-485
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 is a formidable challenge. We present a self-contained and up-to-date d
Externí odkaz:
http://arxiv.org/abs/2402.07273
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 mapping arbitrary nodal values into bound-preserving ones and seeks th
Externí odkaz:
http://arxiv.org/abs/2304.01067
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 generalization is that the choices of the cells to be subdivided are a
Externí odkaz:
http://arxiv.org/abs/1912.13437
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 the structure of a suitably reduced optimality system, we prove that the
Externí odkaz:
http://arxiv.org/abs/1904.07049
Autor:
Kreuzer, Christian, Veeser, Andreas
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 remedy, we devise a new approach where the oscillation has the following
Externí odkaz:
http://arxiv.org/abs/1903.05915
Autor:
Veeser, Andreas, Zanotti, Pietro
We devise variants of classical nonconforming methods for symmetric elliptic problems. These variants differ from the original ones only by transforming discrete test functions into conforming functions before applying the load functional. We derive
Externí odkaz:
http://arxiv.org/abs/1710.03447
Autor:
Veeser, Andreas, Zanotti, Pietro
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 method for linear elasticity, and the quadratic $C^0$ interior penalty me
Externí odkaz:
http://arxiv.org/abs/1710.03452
Autor:
Veeser, Andreas, Zanotti, Pietro
We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optimality constant is determined and the possible impact of nonconformity
Externí odkaz:
http://arxiv.org/abs/1710.03331
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 error in fractional Sobolev spaces, we propose residual-type a posteriori
Externí odkaz:
http://arxiv.org/abs/1507.08247
Autor:
Veeser, Andreas
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 polynomial functions over a simplicial mesh. The main result is that the g
Externí odkaz:
http://arxiv.org/abs/1402.3945