Robuste Adaptive Methoden für singulär gestörte Probleme

• Antragsteller: Professor Dr. Rüdiger Verfürth
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2014 bis 2017
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 260814742

• Erstellungsjahr: 2016

Zusammenfassung der Projektergebnisse

We have obtained a fairly complete picture concerning localization results for several Sobolev norms and reaction-diffusion equations with discontinuous diffusion having either dominant reaction or large jumps of the diffusion. These results allow the efficient and robust (with respect to the critical parameters) use of nonlinear tree approximation. We have not obtained our goals concerning instance or rate-optimality of adaptive finite element methods for these equations. This will be at the focus of our future research. Thus, in summary, we have obtained the goals of our proposal concerning nonlinear approximation by finite element functions but not yet concerning adaptive finite element methods.

Projektbezogene Publikationen (Auswahl)

• Robust localization of the best error with finite elements in the reaction-diffusion norm. Constr. Approx. 42.2 (2015), pp. 313–347
  F. Tantardini, A. Veeser, R. Verfürth
  (Siehe online unter https://doi.org/10.1007/s00365-015-9291-5)