Goal-oriented adaptive space-time finite element methods for regularized parabolic p-Laplace problems

verfasst von

B. Endtmayer, U. Langer, A. Schafelner

Abstract

We consider goal-oriented adaptive space-time finite-element discretizations of the regularized parabolic p-Laplace problem on completely unstructured simplicial space-time meshes. The adaptivity is driven by the dual-weighted residual (DWR) method since we are interested in an accurate computation of some possibly nonlinear functionals at the solution. Such functionals represent goals in which engineers are often more interested than the solution itself. The DWR method requires the numerical solution of a linear adjoint problem that provides the sensitivities for the mesh refinement. This can be done by means of the same full space-time finite element discretization as used for the primal non-linear problems. The numerical experiments presented demonstrate that this goal-oriented, full space-time finite element solver efficiently provides accurate numerical results for different functionals.

Organisationseinheit(en)

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

Externe Organisation(en)

Johannes Kepler Universität Linz (JKU)
Austrian Academy of Sciences

Typ

Artikel

Journal

Computers and Mathematics with Applications

Band

167

Seiten

286-297

Anzahl der Seiten

12

ISSN

0898-1221

Publikationsdatum

01.08.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Modellierung und Simulation, Theoretische Informatik und Mathematik, Computational Mathematics

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2306.07167 (Zugang: Offen)
https://doi.org/10.1016/j.camwa.2024.05.017 (Zugang: Offen)