Saddle point least squares discretization for convection-diffusion

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Author(s)Bacuta, Constantin
Author(s)Hayes, Daniel
Author(s)O'Grady, Tyler
Date Accessioned2024-02-13T20:42:40Z
Date Available2024-02-13T20:42:40Z
Publication Date2023-12-11
DescriptionThis is an Accepted Manuscript of an article published by Taylor & Francis in Applicable Analysis on 12/11/2023, available at: https://doi.org/10.1080/00036811.2023.2291511. © 2023 Informa UK Limited, trading as Taylor & Francis Group. This article will be embargoed until 12/11/2024.
AbstractWe consider a model convection-diffusion problem and present our recent analysis and numerical results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the problem. Using the concepts of optimal norm and saddle point reformulation, we found new error estimates for the case of uniform meshes. We compare the standard linear Galerkin discretization to a saddle point least square discretization that uses quadratic test functions, and explain the non-physical oscillations of the discrete solutions. We also relate a known upwinding Petrov–Galerkin method and the stream-line diffusion discretization method, by emphasizing the resulting linear systems and by comparing appropriate error norms. The results can be extended to the multidimensional case in order to find efficient approximations for more general singular perturbed problems including convection dominated models.
SponsorThe work was supported by the NSF-DMS [grant number 2011615].
CitationBacuta, Constantin, Daniel Hayes, and Tyler O’Grady. “Saddle Point Least Squares Discretization for Convection-Diffusion.” Applicable Analysis, December 11, 2023, 1–28. https://doi.org/10.1080/00036811.2023.2291511.
ISSN1563-504X
URLhttps://udspace.udel.edu/handle/19716/33984
Languageen_US
PublisherApplicable Analysis
Keywordsleast squares
Keywordssaddle point systems
Keywordsup-winding Petrov Galerkin
Keywordsoptimal stability norm
Keywordsconvection dominated problem
TitleSaddle point least squares discretization for convection-diffusion
TypeArticle
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