Asymptotic behavior and finite element error estimates of Kelvin-Voigt viscoelastic fluid flow model

A rotational velocity‐correction projection method for the Kelvin–Voigt viscoelastic fluid equations

“…By using the semi‐discrete Galerkin method, the optimal error estimates of this model in $$$ {L}^2 $$$ and $$$ {H}^1 $$$ were obtained in Bajpai et al and Pany et al 9,10 The numerical solution algorithm has been introduced for the initial boundary problem of the Kelvin–Voigt model by using the explicit format with seven order of Runge–Kutta type in Kadchenko and Kondyukov 11 . Considering linearized backward Euler method, Bajpai and Amiya et al derived the optimal error estimates and obtained that the results are valuable when the Kelvin–Voigt converges to the Navier–Stokes system in Kundu et al 12 In Antontsev et al, 13 the authors studied the generalized K‐V system and proved that the weak solution is existent. By using the space‐time finite element method and Euler semi‐implicit scheme, Zhang and Duan 14 obtained the stability and convergence analysis of the Kelvin–Voigt model by using the multilevel space‐time finite element method; at the same time, error estimate of this model was established.…”

Stability and convergence analysis of a semi-implicit fractional FEM-scheme for non-Newtonian fluid flows of polymer aqueous solutions with fractional time-derivative

“…In recent years, the main mathematical challenges for researchers are dealing with nonlinear partial differential equations. Consequently, for the case of fluid equations there have been many attempts to develop new methods to obtain numerical solutions for non-linear types of equations using classical and hybrid techniques (Kundu et al 2017;Pany 2017). On the other hand, the fractional derivative has been of a great importance in the mathematical modeling of many physical and engineering problems, such as non-Newtonian fluids (Bakhti et al 2017), visco-elasticity (Pirrotta et al 2015) and material science in general Baleanu 2016, 2015).…”

A fully discrete finite element scheme for the Kelvin-Voigt model

“…Secondly, for numerical methods, the finite element analysis of (1) has been studied in many articles. In [16], semidiscrete approximation for (1) is discussed, keeping the time variable continuous. Moreover, Pany et al [25] have derived a priori optimal error estimates for the velocity in L ∞ (L 2 ) norm as well as velocity in L ∞ (H 1 ) norm and for the pressure term in L ∞ (L 2 ) norm.…”