Anisotropic space-time goal-oriented error control and mesh adaptivity for convection-diffusion-reaction equations

Bause, Markus; Bruchhäuser, Marius Paul; Endtmayer, Bernhard; Margenberg, Nils; Toulopoulos, Ioannis; Wick, Thomas

doi:10.48550/arXiv.2504.04951

Anisotropic space-time goal-oriented error control and mesh adaptivity for convection-diffusion-reaction equations

Publication date

2025-04-07

Document type

Preprint

Author

Bause, Markus

Bruchhäuser, Marius Paul

Endtmayer, Bernhard

Margenberg, Nils

Toulopoulos, Ioannis

Wick, Thomas

Organisational unit

Numerische Mathematik

DOI

10.48550/arXiv.2504.04951

URI

https://openhsu.ub.hsu-hh.de/handle/10.24405/20992

Publisher

arXiv

Part of the university bibliography

✅

Language

English

Abstract

We present an anisotropic goal-oriented error estimator based on the Dual Weighted Residual (DWR) method for time-dependent convection-diffusion-reaction (CDR) equations. Using anisotropic interpolation operators the estimator is elementwise separated with respect to the single directions in space and time leading to adaptive, anisotropic mesh refinement in a natural way. 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. Efficiency and robustness of the underlying algorithm are demonstrated for different goal functionals. The directional error indicators quantify anisotropy of the solution with respect to the goal, and produce meshes that efficiently capture sharp layers. Numerical examples show the superiority of the proposed approach over isotropic adaptive and global mesh refinement 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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Submitted version under review

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