Talks and Poster Presentations (without Proceedings-Entry):
G. Gantner, D. Haberlik, D. Praetorius:
"Axioms of adaptivity revisited: Optimal adaptive IGAFEM";
Talk: WONAPDE 2019 - Sixth Chilean Workshop on Numerical Analysis of Partial Differential Equations,
The axioms of adaptivity from [C. Carstensen, M. Feischl, M. Page, D. Praetorius. Axioms of adaptivity. Computers & Mathematics with Applications, 67, 1195-1253, 2014] analyze under which assumptions on the a posteriori error estimator and the mesh-refinement strategy, a mesh re fining adaptive algorithm yields convergence with optimal algebraic rates. In our talk, which is based on our recent work [G. Gantner, D. Haberlik, D. Praetorius. Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines. Mathematical Models and Methods in Applied Sciences, 27, 2631-2674, 2017], we now address the question which properties of the FEM are sufficient to ensure that the usual weighted-residual error estimator is well-defined and satisfies the axioms of adaptivity. In particular, our analysis covers conforming FEM in the framework of isogeometric analysis with hierarchical splines.
Created from the Publication Database of the Vienna University of Technology.