Saddle point least squares discretization for convection-diffusion
Date
2023-12-11
Journal Title
Journal ISSN
Volume Title
Publisher
Applicable Analysis
Abstract
We 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.
Description
This 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.
Keywords
least squares, saddle point systems, up-winding Petrov Galerkin, optimal stability norm, convection dominated problem
Citation
Bacuta, 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.