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000641892 0247_ $$2arXiv$$aarXiv:2507.00723
000641892 0247_ $$2datacite_doi$$a10.3204/PUBDB-2025-05238
000641892 037__ $$aPUBDB-2025-05238
000641892 041__ $$aEnglish
000641892 088__ $$2arXiv$$aarXiv:2507.00723
000641892 1001_ $$0P:(DE-HGF)0$$aBause, Markus$$b0$$eCorresponding author
000641892 245__ $$aMulti-goal-oriented anisotropic error control and mesh adaptivity for time-dependent convection-dominated problems
000641892 260__ $$c2025
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000641892 500__ $$a14 pages, 5 Figures, 2 Tables. Submitted to PAMM. arXiv admin note: substantial text overlap with arXiv:2504.04951
000641892 520__ $$aIn 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.
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000641892 7001_ $$0P:(DE-HGF)0$$aBruchhäuser, Marius Paul$$b1
000641892 7001_ $$0P:(DE-HGF)0$$aEndmayer, Bernhard$$b2
000641892 7001_ $$0P:(DE-H253)PIP1100991$$aMargenberg, Nils$$b3
000641892 7001_ $$0P:(DE-HGF)0$$aToulopoulos, Ioannis$$b4
000641892 7001_ $$0P:(DE-HGF)0$$aWick, Thomas$$b5
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