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Duan, Mengmeng; Yang, Yan; Feng, Minfu

A weak Galerkin finite element method for the Kelvin-Voigt viscoelastic fluid flow model. (English) Zbl 1505.65261

Appl. Numer. Math. 184, 406-430 (2023).
Summary: In this paper, we consider a weak Galerkin finite element method for the Kelvin-Voigt viscoelastic fluid flow model. Firstly, the weak Galerkin finite element method is used to approximate the spatial variable and we use piecewise polynomials of degrees \(k\), \(k - 1\) and \(k - 1\) (\(k \geq 1\)) to approximate the velocity, pressure, and the numerical trace of the velocity on the interfaces of elements, respectively. Secondly, the backward Euler difference method is adopted in the temporal discretization for the fully discrete scheme. Furthermore, the stability and optimal convergence of numerical solutions in \(L^\infty( L^2)\) and \(L^\infty( H^1)\)-norms of velocity as well as \(L^\infty( L^2)\)-norm of pressure were presented. Finally, numerical examples verify the effectiveness of the proposed method, which also obtain that the algorithm has convergence and robust for different retardation time.

Cited in 3 Documents

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
76A10 Viscoelastic fluids
76M10 Finite element methods applied to problems in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
35Q35 PDEs in connection with fluid mechanics

Keywords:

weak Galerkin; finite element method; Kelvin-Voigt model; error estimates
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References:

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