Uniform Convergence Analysis For EQ₁^rot Nonconforming Finite Element Approximation To Advection-diffusion Equations And Numerical Results

In this paper,the EQ₁^rotnonconforming finite element approximation to the nonlinear advection-diffusion equations with unsteady coefficients is discussed.By using integral identities and aver-aging techniques,and with the help of the EQ₁^rotelement's two important properties:?1?For the EQ₁^rotfinite element,when the exact solution of the equation is in the Sobolev space H³??,the compatible error of the finite element solution can reach the order of O?h²?,which is more than its Sobolev space The interpolation error is one order higher;?2?When using EQ₁^rotelement,the Ritz projection operator is equivalent to its interpolation operator.From these we have obtained the optimal uniform error estimate for the diffusion parameter appearing in the equation.In addition,the finite element method and the meshless method are also used to discuss the numerical solution of the convection-diffusion equation.Text The meshless virtual center point Kansa method used in the method is different from the traditional Kansa method.The traditional Kansa method Place the centers in the enclosed area of??the area in question,and these centers can be located outside them.Also uses a These methods determine the shape parameters in the radial basis function.And apply these methods to the convection-diffusion equation and calculate The result is very accurate.