Publications in Scientific Journals:
P. Heid, D. Praetorius, T. Wihler:
"Energy contraction and optimal convergence of adaptive iterative linearized finite element methods";
Computational Methods in Applied Mathematics,
21
(2021),
2;
407
- 422.
English abstract:
In this note, we revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert spaces. Our key observation is that the general approach from [Heid, Wihler (2020)]
satisfies an energy contraction property in the context of (abstract) strongly monotone problems. This property, in turn, is the crucial ingredient in the recent convergence analysis in [Gantner et al. (2020)]. In particular, we deduce that adaptive iterative linearized finite element methods (AILFEMs) lead to linear convergence with optimal algebraic rates with respect to the degrees of freedom as well as the total computational time.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1515/cmam-2021-0025
Created from the Publication Database of the Vienna University of Technology.