Numerical modeling of viscoelastic flows using equal low-order finite elements

Variational multi-scale stabilized formulations for the stationary three-field incompressible viscoelastic flow problem

“…It is observed that the size of the vortex appearing in the bottom corner decreases as We increases. This is consistent with the results reported in the literature [8,10,33,34].…”

“…For We > 2.5 it appears clearly defined (both in the M3 and in the M2-M5 meshes) with a bigger size in the more elastic cases. This is perfectly consistent with the results published by Li et al [8] and the sizes of the vortex are very close to the values reported by Nithiarasu [10]. Fig.…”

“…A possible remedy to this situation is to enrich the finite element spaces for the velocity and the stress in order to satisfy both restrictions [5,17]. Another possibility is to use stabilized formulations permitting any interpolation for the variables [8,2,7], which is the approach we pursue in this paper. In general, a stabilized formulation consists of replacing B in (5) by another semilinear form B h , possibly mesh dependent, with better stability properties.…”

A new difference scheme for fractional cable equation and stability analysis

“…The values of the functions u and f at the grid points are denoted u k j = u(x j , t k ) and f k j = f (x j , t k ), respectively. Let u(x, t), u t (x, t) and u tt (x, t) are continuous on [0,1].…”

A new difference scheme for time fractional heat equations based on the Crank-Nicholson method

“…Due to their ability to model more adequately some phenomena, fractional partial differential equations (FPDEs) have been used in numerous areas such as viscoelasticity [3,15], finance [28,30], hydrology and porous media [4,9], engineering [16,26], control systems [18], etc. c 2013 Diogenes Co., Sofia pp.…”