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A quadratic equal‐order stabilized method for Stokes problem based on two local Gauss integrations
Author(s) -
Zheng Haibiao,
Shan Li,
Hou Yanren
Publication year - 2010
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.20486
Subject(s) - mathematics , gauss , quadratic equation , finite element method , compressibility , mathematical analysis , stability (learning theory) , partial derivative , simple (philosophy) , element (criminal law) , partial differential equation , space (punctuation) , residual , order (exchange) , geometry , algorithm , law , physics , philosophy , epistemology , quantum mechanics , machine learning , computer science , political science , thermodynamics , linguistics , finance , economics
In this article, we analyze a quadratic equal‐order stabilized finite element approximation for the incompressible Stokes equations based on two local Gauss integrations. Our method only offsets the discrete pressure gradient space by the residual of the simple and symmetry term at element level to circumvent the inf‐sup condition. And this method does not require specification of a stabilization parameter, and always leads to a symmetric linear system. Furthermore, this method is unconditionally stable, and can be implemented at the element level with minimal additional cost. Finally, we give some numerical simulations to show good stability and accuracy properties of the method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010