TY  - EJOUR
AU  - Bause, Markus
AU  - Bruchhäuser, Marius Paul
AU  - Endmayer, Bernhard
AU  - Margenberg, Nils
AU  - Toulopoulos, Ioannis
AU  - Wick, Thomas
TI  - Multi-goal-oriented anisotropic error control and mesh adaptivity for time-dependent convection-dominated problems
IS  - arXiv:2507.00723
M1  - PUBDB-2025-05238
M1  - arXiv:2507.00723
PY  - 2025
N1  - 14 pages, 5 Figures, 2 Tables. Submitted to PAMM. arXiv admin note: substantial text overlap with arXiv:2504.04951
AB  - 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.
LB  - PUB:(DE-HGF)25
DO  - DOI:10.3204/PUBDB-2025-05238
UR  - https://bib-pubdb1.desy.de/record/641892
ER  -