Numerical Modeling and Open-Source Implementation of Variational Partition-of-Unity Localizations of Space-Time Dual-Weighted Residual Estimators for Parabolic Problems

authored by

J. P. Thiele, T. Wick

Abstract

In this work, we consider space-time goal-oriented a posteriori error estimation for parabolic problems. Temporal and spatial discretizations are based on Galerkin finite elements of continuous and discontinuous type. The main objectives are the development and analysis of space-time estimators, in which the localization is based on a weak form employing a partition-of-unity. The resulting error indicators are used for temporal and spatial adaptivity. Our developments are substantiated with several numerical examples.

Organisation(s)

Institute of Applied Mathematics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines

Type

Article

Journal

Journal of scientific computing

Volume

99

ISSN

0885-7474

Publication date

04.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Software, Engineering(all), Computational Mathematics, Theoretical Computer Science, Applied Mathematics, Numerical Analysis, Computational Theory and Mathematics

Electronic version(s)

https://doi.org/10.1007/s10915-024-02485-6 (Access: Open)