A PRIORI ERROR ANALYSIS OF MIXED FEM FOR STOKES PROBLEM WITH VARIABLE VISCOSITY

Abstract

In this paper study of the stress-velocity finite formulation of the Arnold- Winther (A-W) mixed finite element method (MFEM) for two-dimensional (2-D) stokes source problem is analysed. The source stokes problem with changing viscosity which is a function and varies spatially or geometrically is described together with an a priori error estimation. The model problem in this work is supplied to us in velocity-pressure form, so we first use deviatoric stress tensors to help us transform the pressure-velocity problem into a stressvelocity formulation. Next, we establish the well-posedness of the solution to the stokes problem in both continuous and discrete form by deriving its weak formulation and deriving the mixed discrete finite element method . In this study, we define the mixed finite element approach for the Stokes problem and discretize the domain.Next, we analyse the error for the approach and extract the priori error estimates for the Stokes source problem. In this study the discretization of finite element of lowest order is defined and by analysing the lowest order, we can define the same for the highest order elements. This A priori error analysis provides the stability and reliability of our earlier solution. In order to maintain accuracy, we estimate the solution and analyse the accuracy of the solution for the source Stokes problem with changing viscosity in this work. We also analyse the order of convergence and error estimations.