Well-posedness and a numerical study of a regularization model with adaptive nonlinear filtering for incompressible fluid flow. (June 2016)

• Record Type: Journal Article
• Authors: Cao, Yanzhao; Chen, Song; Rebholz, Leo G.
• Is Part Of: Computers & mathematics with applications. Volume 71:issue 11(2016)
• Page Start: 2192
• Page End: 2205
• Publication Date: 2016-06
• Subjects: Navier–Stokes Equations -- Nonlinear filtering -- Finite element; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2015.12.012
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We give a detailed analytical study of a Leray model of incompressible flow that uses nonlinear filtering based on indicator functions. The indicator functions allow for local regularization, instead of global regularization which can over-smooth and dampen out important flow structures. The key to the analysis is the identification of the indicator function as a Nemyskii operator. After proving well-posedness, we provide a numerical study which includes proving optimal convergence of finite element method for the model, as well as several numerical experiments.