| Summary: | In this work, numerical schemes for the generalized stationary regularized viscoplastic fluids equations with highly nonlinear viscosities are analyzed. The discretisation using certain high order finite elements (Q2P1disc) is achieved to transform the nonlinear continuous form to the corresponding nonlinear discretized one. The solution process is analyzed in the sense of successive continuous Newton method (CNM) with minimal residual method as a linear solver. The convergence of the method is proved using the sense of the minimization technique due to the monotone decreasing feature of their viscosities. It is shown that, the convergence process of the successive nonlinear iterative method is mostly approaching a semi-quadratic behavior for slow flow cases. The numerical tests are achieved to have good fitting with the theoretical results using a self implemented Matlab code for the interested problem. Keywords: Generalized viscoplastic fluid, Finite element method, Posteriori error estimate, Newton iterative method, Minimum residual method
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