COMPARISON OF VARIATIONAL DISCRETIZATIONS FOR A CONVECTION-DIFFUSION PROBLEM.

BACUTA, CONSTANTIN; BACUTA, CRISTINA; HAYES, DANIEL

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 finding representations of the optimal norms on the trial spaces at the continuous and discrete levels. We analyze and compare three methods: the standard linear discretization, the saddle point least square and the 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 multi-dimensional cases.

LEAST squares; SADDLERY

Romanian Journal of Pure & Applied Mathematics / Revue Roumaine de Mathematiques Pures et Appliquees, 2024, Vol 69, Issue 3/4, p327

0035-3965

Academic Journal

10.59277/RRMPA.2024.327.351