A Posteriori Error Estimates For Variational Inequalities Of The Second Kind

In this paper,we take frictional contact problem as an example to study of a posteriori error estimation for variational inequlity problems of the second kind.Firstly,we briefly introduce the research background and the research status of variational inequality problems and related definitions and theorems.Secondly,Lagrange multiplier method is used to transform an inequlity problem to a linear equation,and then the discrete form of the finite element method is presented.We,respectively,adopte hierarchical bases method and the solution of auxiliary local problem implicit estimation method to deal with variational problem,and analyse a posteriori error estimation of frictional contact problem,then a lower and upper bound of the error estimation is deduced.In the end,we make a summary of this thesis,and then point out the study direction for the future.