AN AUGMENTED MIXED FINITE ELEMENT METHOD FOR THE NAVIER-STOKES EQUATIONS WITH VARIABLE VISCOSITY

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10334915" target="_blank" >RIV/00216208:11320/16:10334915 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1137/15M1013146" target="_blank" >http://dx.doi.org/10.1137/15M1013146</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/15M1013146" target="_blank" >10.1137/15M1013146</a>

Result language

angličtina

Original language name

AN AUGMENTED MIXED FINITE ELEMENT METHOD FOR THE NAVIER-STOKES EQUATIONS WITH VARIABLE VISCOSITY

Original language description

A new mixed variational formulation for the Navier-Stokes equations with constant density and variable viscosity depending nonlinearly on the gradient of velocity, is proposed and analyzed here. Our approach employs a technique previously applied to the stationary Boussinesq problem and to the Navier-Stokes equations with constant viscosity, which consists firstly of the introduction of a modified pseudostress tensor involving the diffusive and convective terms, and the pressure. Next, by using an equivalent statement suggested by the incompressibility condition, the pressure is eliminated, and in order to handle the nonlinear viscosity, the gradient of velocity is incorporated as an auxiliary unknown. Furthermore, since the convective term forces the velocity to live in a smaller space than usual, we overcome this difficulty by augmenting the variational formulation with suitable Galerkin-type terms arising from the constitutive and equilibrium equations, the aforementioned relation defining the additional unknown, and the Dirichlet boundary condition. The resulting augmented scheme is then written equivalently as a fixed point equation, and hence the well-known Schauder and Banach theorems, combined with classical results on bijective monotone operators, are applied to prove the unique solvability of the continuous and discrete systems. No discrete inf-sup conditions are required for the well-posedness of the Galerkin scheme, and hence arbitrary finite element subspaces of the respective continuous spaces can be utilized. In particular, given an integer k >= 0, piecewise polynomials of degree <= k for the gradient of velocity, Raviart-Thomas spaces of order k for the pseudostress, and continuous piecewise polynomials of degree <= k+1 for the velocity, constitute feasible choices.

Czech name

—

Czech description

—

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

—

Project

<a href="/en/project/LL1202" target="_blank" >LL1202: Implicitly constituted material models: from theory through model reduction to efficient numerical methods</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2016

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

SIAM Journal on Numerical Analysis

ISSN

0036-1429

e-ISSN

—

Volume of the periodical

54

Issue of the periodical within the volume

2

Country of publishing house

US - UNITED STATES

Number of pages

24

Pages from-to

1069-1092

UT code for WoS article

—

EID of the result in the Scopus database

2-s2.0-84970939115