The Super-Convergence in Rheological Flow

To estimate the solution of the coupled first-order hyperbolic partial differential equations, we use both the boundary-layer method and numeric analysis to study the Cauchy fluid equations and P-T/T stress equation. On the macroscopic scale the free surface elements generate flow singularity and stress uncertainty by excessive tensile stretch. A numerical super-convergence semi-discrete finite element scheme is used to solve the time dependent equations. The coupled nonlinear solutions are estimated by boundary-layer approximation. Its numerical super convergence is proposed with the a priori and a posteriori error estimates.