Comparison of variational discretizations for a convection-diffusion problem
Abstract
For a model convection-diffusion problem, we obtain new error estimates for a general upwinding finite element discretization based on bubble modification of the test space. The key analysis tool is based on finding representations of the optimal norms on the trial spaces at the continuous and discrete levels. We analyze and compare the standard linear discretization, the saddle point least square and upwinding Petrov-Galerkin methods. We conclude that the bubble upwinding Petrov-Galerkin method is the most performant discretization for the one dimensional model. Our results for the model convection-diffusion problem can be extended for creating new and efficient discretizations for the multidimensional cases.
Cite
@article{arxiv.2402.10281,
title = {Comparison of variational discretizations for a convection-diffusion problem},
author = {Constantin Bacuta and Cristina Bacuta and Daniel Hayes},
journal= {arXiv preprint arXiv:2402.10281},
year = {2024}
}
Comments
22 pages, no figures. arXiv admin note: text overlap with arXiv:2402.03314