ANALYSIS OF AN AUGMENTED MIXED-FEM FOR THE NAVIER-STOKES PROBLEM
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10371178" target="_blank" >RIV/00216208:11320/17:10371178 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1090/mcom/3124" target="_blank" >http://dx.doi.org/10.1090/mcom/3124</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/mcom/3124" target="_blank" >10.1090/mcom/3124</a>
Alternative languages
Result language
angličtina
Original language name
ANALYSIS OF AN AUGMENTED MIXED-FEM FOR THE NAVIER-STOKES PROBLEM
Original language description
In this paper we propose and analyze a new augmented mixed finite element method for the Navier-Stokes problem. Our approach is based on the introduction of a "nonlinear-pseudostress" tensor linking the pseudostress tensor with the convective term, which leads to a mixed formulation with the nonlinear-pseudostress tensor and the velocity as the main unknowns of the system. Further variables of interest, such as the fluid pressure, the fluid vorticity and the fluid velocity gradient, can be easily approximated as a simple postprocess of the finite element solutions with the same rate of convergence. The resulting mixed formulation is augmented by introducing Galerkin least-squares type terms arising from the constitutive and equilibrium equations of the Navier-Stokes equations and from the Dirichlet boundary condition, which are multiplied by stabilization parameters that are chosen in such a way that the resulting continuous formulation becomes well-posed. Then, the classical Banach fixed point theorem and the Lax-Milgram lemma are applied to prove well-posedness of the continuous problem. Similarly, we establish well-posedness and the corresponding Cea estimate of the associated Galerkin scheme considering any conforming finite element subspace for each unknown. In particular, the associated Galerkin scheme can be defined by employing Raviart-Thomas elements of degree k for the nonlinear-pseudostress tensor and continuous piecewise polynomial elements of degree k + 1 for the velocity, which leads to an optimal convergent scheme. In addition, we provide two iterative methods to solve the corresponding nonlinear system of equations and analyze their convergence. Finally, several numerical results illustrating the good performance of the method are provided.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
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
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematics of Computation
ISSN
0025-5718
e-ISSN
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Volume of the periodical
86
Issue of the periodical within the volume
304
Country of publishing house
US - UNITED STATES
Number of pages
27
Pages from-to
589-615
UT code for WoS article
000391546700004
EID of the result in the Scopus database
2-s2.0-85008462126