Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Oberseminar Numerische Mathematik

 

Dr. Gregor Gantner
Technische Universität Wien

 
spricht am
 
Dienstag, 16. Oktober 2018
 
um
 
16:00 Uhr
 
im
 
Raum 1008 (L1)
 
über das Thema:
 

» Adaptive Isogeometric Methods with Optimal Convergence Rates«

Abstract:
The CAD standard for spline representation in 2D or 3D relies on tensor-product splines. To allow for adaptive refinement, several extensions have emerged, e.g., analysis-suitable T-splines, hierarchical splines, or LR-splines. All these concepts have been studied via numerical experiments, but there exists only little literature concerning the thorough analysis of adaptive isogeometric methods. In [Gantner, Haberlik, Praetorius, Math. Models Methods Appl. Sci. 27 (2017)] , we investigate linear convergence at optimal algebraic rate of the weighted-residual error estimator (or equivalently: energy error plus data oscillations) of an isogeometric finite element method (IGAFEM) with hierarchical B-splines. In particular, we propose a refinement strategy to generate a sequence of refined meshes and corresponding discrete solutions. Usually, CAD provides only a parametrization of the boundary instead of the domain itself. The boundary element method circumvents this difficulty by working only on the CAD provided boundary mesh. In 2D, our adaptive algorithm steers the mesh-refinement and the local smoothness of the ansatz functions. Recently, we proved linear convergence at optimal algebraic rate of the employed weighted-residual estimator in [Feischl, Gantner, Haberl, Praetorius, Numer. Math. 136 (2017)]. In 3D, we consider an adaptive IGABEM with hierarchical splines and prove linear convergence of the estimator at optimal rate; see [Gantner, PhD thesis at TU Wien (2017)].

 

Hierzu ergeht herzliche Einladung.
Prof. Dr. Daniel Peterseim



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