FEM For Non-newtonian Fluid Models And Error Estimation Of Simpson Integral Rule

In this paper,we study the finite element method for non-Newtonian fluid model,and obtain some error estimates for Simpson integral rule.First of all,for the complex surface contact problem,we establish the fluidstructure interaction P-T/T equations.We make approximate process on the nonlinear term,and based on the difference method and the basic principle of the finite element,we obtain the component forms of the original coupling equations.For the space domain,we use sixteen-point-bicubic element to construct shape functions.For the time domain,we make calculations by utilizing three difference schemes-Euler scheme,Crank-Nicolson scheme and Adams scheme.By using matlab mathematical software,we get the stress and strain of the 3 × 3 grid when it receives a forced boundary movement by right upper oblique 45 degrees.Secondly,we introduce the problem(Q),which is equivalent to Cauchy equation.Based on the theory of Sobolev space,finite difference and finite element method,we analyze the error introduced by finite element semi discretization in space of sixteen-point-bicubic shape functions.And we also analyze the error introduced by difference in time of Euler scheme,Crank-Nicolson scheme and Adams scheme.Then,through the numerical simulation,we make a comparison on the error of the last two fully-discrete schemes.Thirdly,in the calculation of fluid-solid coupling equations,we use the nonequidistant nodes on the space domain-zeroes of quintic Lobatto polynomial as the nodes to structure shape functions by Lagrange interpolation.For the time domain,we still use the above three difference schemes.By using Matlab mathematical software,we get the results of numerical simulation in the different computing schemes.Finally,we turn our attention to the error estimates of Simpson numerical integration.The error estimates of numerical integration are closely related to the precision of finite element calculation.For a special class of functions-the second class s-convex functions(covering all convex functions),we establish a series of inequalities for the third-order and fourth-order estimates of the Simpson integral rule.Some applications are also obtained.