Preprint

PUBDB-2025-05238

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Multi-goal-oriented anisotropic error control and mesh adaptivity for time-dependent convection-dominated problems

Bause, M. (Corresponding author) ; Bruchhäuser, M. P. ; Endmayer, B. ; Margenberg, N.Extern* ; Toulopoulos, I. ; Wick, T.

2025

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Please use a persistent id in citations: doi:10.3204/PUBDB-2025-05238

Report No.: arXiv:2507.00723

Abstract: In this work, we present an anisotropic multi-goal error control based on the Dual Weighted Residual (DWR) method for time-dependent convection-diffusion-reaction (CDR) equations. This multi-goal oriented approach allows for an accurate and efficient error control with regard to several quantities of interest simultaneously. Using anisotropic interpolation and restriction operators, we obtain elementwise error indicators in space and time, where the spatial indicators are additionally separated with respect to the single directions. The directional error indicators quantify anisotropy of the solution with respect to the goals, and produce adaptive, anisotropic meshes that efficiently capture layers. To prevent spurious oscillations the streamline upwind Petrov-Galerkin (SUPG) method is applied to stabilize the underlying system in the case of high P\'{e}clet numbers. Numerical examples show efficiency and robustness of the proposed approach for several goal quantities using established benchmarks for convection-dominated transport.

Note: 14 pages, 5 Figures, 2 Tables. Submitted to PAMM. arXiv admin note: substantial text overlap with arXiv:2504.04951

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Contributing Institute(s):

1. Ultrafast Lasers & X-rays Division (FS-CFEL-2)

Research Program(s):

1. 631 - Matter – Dynamics, Mechanisms and Control (POF4-631) (POF4-631)
2. DFG project G:(GEPRIS)390833453 - EXC 2122: PhoenixD: Photonics, Optics, and Engineering – Innovation Across Disciplines (390833453) (390833453)

Experiment(s):

1. AXSIS: Frontiers in Attosecond X-ray Science, Imaging and Spectroscopy

Appears in the scientific report 2025

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