Goal-Oriented Adaptive Space Time Finite Element Methods Applied to Touching Domains

verfasst von

Bernhard Endtmayer, Andreas Schafelner

Abstract

We consider goal-oriented adaptive space-time finite-element discretizations of the parabolic heat equation on completely unstructured simplicial space-time meshes. In some applications, the main interest lies in an accurate computation of some possibly nonlinear functionals at the solution, so called goal functionals. This motivates the use of adaptive mesh refinements driven by the dual-weighted residual (DWR) method. The DWR method requires the numerical solution of a linear adjoint problem which provides information on where the error in the solution has the most influence on the goal functional. This can be done by means of the same full space-time finite element discretization as used for the primal linear problem. The numerical experiment presented demonstrates that this goal-oriented full space-time finite element solver efficiently provides accurate numerical results for a model problem with moving domains and a linear goal functional.

Organisationseinheit(en)

Institut für Angewandte Mathematik
PhoenixD: Simulation, Fabrikation und Anwendung optischer Systeme

Externe Organisation(en)

Johannes Kepler Universität Linz (JKU)

Typ

Aufsatz in Konferenzband

Seiten

340-349

Anzahl der Seiten

10

Publikationsdatum

28.04.2025

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Modellierung und Simulation, Allgemeiner Maschinenbau, Diskrete Mathematik und Kombinatorik, Steuerung und Optimierung, Computational Mathematics

Elektronische Version(en)

https://doi.org/10.1007/978-3-031-86169-7_35 (Zugang: Geschlossen)
https://doi.org/10.48550/arXiv.2401.17237 (Zugang: Offen)