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

authored by: 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.
Organisation(s): Institute of Applied Mathematics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines
External Organisation(s): Johannes Kepler University of Linz (JKU)
Austrian Academy of Sciences
Type: Article
Journal: Computers and Mathematics with Applications
Volume: 167
Pages: 286-297
No. of pages: 12
ISSN: 0898-1221
Publication date: 01.08.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Modelling and Simulation, Computational Theory and Mathematics, Computational Mathematics
Electronic version(s): https://doi.org/10.48550/arXiv.2306.07167 (Access: Open)
https://doi.org/10.1016/j.camwa.2024.05.017 (Access: Open)