Moving Mesh with Streamline Upwind Petrov-Galerkin (MM-SUPG) Method for Time-dependent Convection-Dominated Convection-Diffusion Problems

[2105.08765] Moving Mesh with Streamline Upwind Petrov-Galerkin (MM-SUPG) Method for Time-dependent Convection-Dominated Convection-Diffusion Problems Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2105.08765 (math) [Submitted on 18 May 2021 ( v1 ), last revised 14 Apr 2026 (this version, v4)] Title: Moving Mesh with Streamline Upwind Petrov-Galerkin (MM-SUPG) Method for Time-dependent Convection-Dominated Convection-Diffusion Problems Authors: Xianping Li , Matthew McCoy View a PDF of the paper titled Moving Mesh with Streamline Upwind Petrov-Galerkin (MM-SUPG) Method for Time-dependent Convection-Dominated Convection-Diffusion Problems, by Xianping Li and Matthew McCoy View PDF HTML (experimental) Abstract: Time-dependent convection-dominated convection-diffusion problems are considered. We develop a moving mesh streamline upwind Petrov-Galerkin (MM-SUPG) method by combining residual-based SUPG stabilization with a metric-based moving mesh PDE (MMPDE) approach. The key feature of the method is the interaction between mesh adaptation and stabilization: the evolving mesh modifies both the direction and magnitude of the SUPG stabilization through the local element geometry, while stabilization improves robustness in convection-dominated regimes. For isotropic diffusion, numerical results show that the proposed method reduces spurious oscillations and provides improved resolution of sharp layers compared with fixed mesh methods, while yielding accuracy comparable to moving mesh finite element methods without SUPG in some cases. For anisotropic diffusion, we introduce a weighted tensor that incorporates both the diffusion tensor and the convection field, and construct a metric tensor via intersection to guide mesh adaptation. Under suitable assumptions on the elementwise tensors and mesh geometry, we establish sufficient conditions for the discrete maximum principle (DMP) of the fully discrete scheme. The analysis is based on quantitative bounds for the convection terms, and requires structural conditions on the alignment between the velocity field and the diffusion tensor. Numerical experiments demonstrate that the proposed metric improves monotonicity properties and reduces undershoots, while maintaining overall accuracy. Comments: There are 36 pages, 13 figures, and 5 tables Subjects: Numerical Analysis (math.NA) MSC classes: 65M50, 65M60 Cite as: arXiv:2105.08765 [math.NA] (or arXiv:2105.08765v4 [math.NA] for this version) https://doi.org/10.48550/arXiv.2105.08765 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Xianping Li [ view email ] [v1] Tue, 18 May 2021 18:31:19 UTC (5,662 KB) [v2] Tue, 1 Jun 2021 21:23:53 UTC (5,657 KB) [v3] Mon, 20 May 2024 22:48:57 UTC (3,027 KB) [v4] Tue, 14 Apr 2026 02:35:01 UTC (2,929 KB) Full-text links: Access Paper: View a PDF of the paper titled Moving Mesh with Streamline Upwind Petrov-Galerkin (MM-SUPG) Method for Time-dependent Convection-Dominated Convection-Diffusion Problems, by Xianping Li and Matthew McCoy View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2021-05 Change to browse by: cs cs.NA math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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