A posteriori single-and multi-goal error control and adaptivity for partial differential equations

B Endtmayer, U Langer, T Richter, A Schafelner… - arXiv preprint arXiv …, 2024 - arxiv.org
This work reviews goal-oriented a posteriori error control, adaptivity and solver control for
finite element approximations to boundary and initial-boundary value problems for stationary …

[HTML][HTML] Goal-oriented adaptive space-time finite element methods for regularized parabolic p-laplace problems

B Endtmayer, U Langer, A Schafelner - Computers & Mathematics with …, 2024 - Elsevier
We consider goal-oriented adaptive space-time finite-element discretizations of the
regularized parabolic p-Laplace problem on completely unstructured simplicial space-time …

Quasi-Newton variable preconditioning for nonlinear nonuniformly monotone elliptic problems posed in Banach spaces

B Borsos, J Karátson - IMA Journal of Numerical Analysis, 2022 - academic.oup.com
Quasi-Newton-type iterative solvers are developed for a wide class of nonlinear elliptic
problems. The presented generalization of earlier efficient methods covers various …

[HTML][HTML] Multigoal-oriented optimal control problems with nonlinear PDE constraints

B Endtmayer, U Langer, I Neitzel, T Wick… - … & Mathematics with …, 2020 - Elsevier
In this work, we consider an optimal control problem subject to a nonlinear PDE constraint
and apply it to a semi-linear monotone PDE and the regularized p-Laplace equation. To this …

Locally different models in a checkerboard pattern with mesh adaptation and error control for multiple quantities of interest

B Endtmayer - PAMM, 2024 - Wiley Online Library
In this work, we apply multi‐goal oriented error estimation to the finite element method. In
particular, we use the dual weighted residual method and apply it to a model problem. This …

A multi-mesh approach for accurate computation of multi-target functionals in aerodynamics design

G Hu, R Li, J Wang - arXiv preprint arXiv:2406.14992, 2024 - arxiv.org
Aerodynamic optimal design is crucial for enhancing performance of aircrafts, while
calculating multi-target functionals through solving dual equations with arbitrary right-hand …

Quasi-Newton type iterative solution of nonlinear elliptic PDEs with non-uniform monotonicity conditions

B Borsos - 2021 - search.proquest.com
To construct quasi-Newton methods, a general approach to has been given in [52], where
approximate Jacobians are defined via spectral equivalence, and hence they can be …

Mesh adaptivity and error estimates for optimal control problems and multiple quantities of interest

B Endtmayer, U Langer, I Neitzel, T Wick, W Wollner - wwwpub.zih.tu-dresden.de
In this talk, we derive goal-oriented error estimates and mesh adaptivity for multiple
quantities of interest for optimal control problems with nonlinear constraints [4, 5]. We apply …