A finite element method for the numerical solution of Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivatives

摘要

Abstract Our main aim in the current paper is to find a numerical plan for 2D Rayleigh-Stokes model with fractional derivative on irregular domains such as circular, L-shaped and a unit square with a circular and square hole. The employed fractional derivative is the Riemann-Liou-ville sense. Also, by integrating the equation corresponding to the time variable and then using the Galerkin FEM for the space direction, we obtain a full discrete scheme. The unconditional stability and the convergence estimate of the new scheme have been concluded. Finally, we evaluate results of Galerkin FEM with other numerical methods.