Multi-goal-oriented anisotropic error control and mesh adaptivity for time-dependent convection-dominated problems
Publication date
2025-07-01
Document type
Preprint
Author
Endtmayer Bernhard
Toulopoulos, Ioannis
Wick, Thomas
Organisational unit
Publisher
arXiv
Part of the university bibliography
✅
Language
English
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 Péclet numbers. Numerical examples show efficiency and robustness of the proposed approach for several goal quantities using established benchmarks for convection-dominated transport.
Description
This work is licensed under the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/).
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