Publications in Scientific Journals:
R. Becker, M. Brunner, M. Innerberger, J. Melenk, D. Praetorius:
"Rate-optimal goal-oriented adaptive finite element method for semilinear elliptic PDEs";
Computers and Mathematics with Applications,
118
(2022),
18
- 35.
English abstract:
We formulate and analyze a goal-oriented adaptive finite element method for a semilinear
elliptic PDE and a linear goal functional. The discretization is based on finite elements of
arbitrary (but fixed) polynomial degree and involves a linearized dual problem. The linearization
is part of the proposed algorithm, which employs a marking strategy different to that of
standard adaptive finite element methods. Moreover, unlike the well-known dual-weighted
residual strategy, the analyzed error estimators are completely computable. We prove linear
convergence and, for the first time in the context of goal-oriented adaptivity for nonlinear PDEs,
optimal algebraic convergence rates. In particular, the analysis does not require a sufficiently
fine initial mesh.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1016/j.camwa.2022.05.008
Created from the Publication Database of the Vienna University of Technology.