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Semidiscrete Galerkin method for equations of motion arising in Kelvin‐Voigt model of viscoelastic fluid flow
Author(s) -
Bajpai Saumya,
Nataraj Neela,
Pani Amiya K.,
Damazio Pedro,
Yuan Jin Yun
Publication year - 2013
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.21735
Subject(s) - mathematics , discretization , exponential function , galerkin method , kelvin–voigt material , viscoelasticity , mathematical analysis , finite element method , norm (philosophy) , discontinuous galerkin method , operator (biology) , exponential decay , stokes flow , a priori and a posteriori , flow (mathematics) , physics , geometry , thermodynamics , chemistry , biochemistry , repressor , political science , transcription factor , gene , nuclear physics , law , philosophy , epistemology
Finite element Galerkin method is applied to equations of motion arising in the Kelvin–Voigt model of viscoelastic fluids for spatial discretization. Some new a priori bounds which reflect the exponential decay property are obtained for the exact solution. For optimal L ∞ ( L 2 ) estimate in the velocity, a new auxiliary operator which is based on a modification of the Stokes operator is introduced and analyzed. Finally, optimal error bounds for the velocity in L ∞ ( L 2 ) as well as in L ∞ ( H 0 1 )‐norms and the pressure in L ∞ ( L 2 )‐norm are derived which again preserves the exponential decay property. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013