Investigation of the Oldroyd model as a generalized incompressible Navier–Stokes equation via the interpolating stabilized element free Galerkin technique

Abstract

The main objective of the current paper is to propose a meshless weak form to simulate the Oldroyd equation. At the first stage, the Crank-Nicolson method has been utilized to discreet the temporal direction. At the second stage, the meshless element free Galerkin technique has been employed to approximate the spatial direction. The main equation is a non-local model as there is an integral term in the right hand side of the model. The mentioned integral term is approximated by using a difference scheme. The uniqueness and existence of the proposed numerical plan have been proved by using the Browder fixed point theorem. Furthermore, the error estimation of the developed numerical technique based on the stability and convergence order has been studied. Finally, some examples have been investigated to verify the theoretical results.