Super-penalty Method Based On Morley-Wang-Xu Element Discretization For Fourth Order Elliptic Singular Perturbation Problems

In this study,based on the discontinuous finite element method,the Morley-Wang-Xu element defined by Wang Ming and Xu Jinchao is used to solve the fourth-order elliptic singular perturbation problem.For the variational form of this fourth-order elliptic problem,use super-penalty method,and perform error analysis and numerical simulations.Firstly,when ?=0,the fourth-order elliptic singular perturbation problem is degenerated into the second-order Poisson equation,the super penalty term of Laplace operator is added to the variational form.Under the hypothesis that the exact solution has proper regularity,by using trigonometric inequality,Green formula,Cauchy-Schwarz inequality and the back-tracking inequality,the a priori error analysis of the second-order elliptic problem is carried out.For the second-order problem of posterior error estimation,two operators are defined under the original condition and establish some local lower bound estimators of the posterior error estimation,using some known properties,establish the posterior error estimates of second-order elliptic problems.Then considering the numerical solution of the fourth-order elliptic singular perturbation problem,similar the second-order elliptic problem,the variational form of this fourth-order elliptic problem adds the super penalty term and propose to use Morley-Wang-Xu element methods with super penalty.Under the assumption of exact solution with the lowest regularity,define some related grid norm,establish some local lower bound estimators of error estimate by bubble function technique,and finally establish the error estimate of Morley-Wang-Xu element methods with super penalty for the fourth order elliptic singular perturbation problem.Finally,Morley-Wang-Xu element methods with super penalty for the fourth order elliptic singular perturbation problem,the corresponding result of the example is given in Chapter 4,Section II.