Premium
Local projection FEM stabilization for the time‐dependent incompressible N avier– S tokes problem
Author(s) -
Arndt Daniel,
Dallmann Helene,
Lube Gert
Publication year - 2015
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21944
Subject(s) - mathematics , compressibility , projection (relational algebra) , finite element method , navier–stokes equations , stability (learning theory) , mathematical analysis , nonlinear system , complement (music) , convergence (economics) , partial differential equation , partial derivative , reynolds number , physics , mechanics , algorithm , biochemistry , chemistry , quantum mechanics , machine learning , complementation , computer science , gene , turbulence , economics , thermodynamics , phenotype , economic growth
We consider conforming finite element (FE) approximations of the time‐dependent, incompressible Navier–Stokes problem with inf‐sup stable approximation of velocity and pressure. In case of high Reynolds numbers, a local projection stabilization method is considered. In particular, the idea of streamline upwinding is combined with stabilization of the divergence‐free constraint. For the arising nonlinear semidiscrete problem, a stability and convergence analysis is given. Our approach improves some results of a recent paper by Matthies and Tobiska (IMA J. Numer. Anal., to appear) for the linearized model and takes partly advantage of the analysis in Burman and Fernández, Numer. Math. 107 (2007), 39–77 for edge‐stabilized FE approximation of the Navier–Stokes problem. Some numerical experiments complement the theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1224–1250, 2015