BEM And FEM For Some Kinds Of Elliptic Variational Inequalities

This thesis is composed of two sections. In section one, it analysis the boundary element method of the variational inequality (VI) of the second kind arising in unilateral contact problem with friction term. In section two, twc sorts of finite element method for the fourth-order VI of the second kind are discussed.In section one, a simplified model of a two-dimensional unilateral contact problem with friction is considered, the existence and uniqueness of the corresponding VI of the second kind is disscussed. Its corresponding MRM boundary mixed VI is construct, which provides us the theoretical basis for using element method to solve the mixed VI. Using regularization method, the equivalent variational equation is obtained. By using of its equivalent nonlinear variational equation, it follows the iterative method. Finally it presents the convergence analysis for the approximation solution and discrete approximation solutionIn section two, a fourth-order VI of the second kind arising in a plate frictional bending problem is considered. For the problem, two kinds of finite element methods are analysed. First, using finite element method, the discrete VI is obtained. Abstract error estimate is established in the form of energy norm. Optimal order error estimate of the approximation solution is derived in the form of energy norm. Next, using regularization method, the original problem can be formulated as a differentiable variational equation; the discrete variational equation by finite element method is yielded. Abstract error estimates and error estimates of the approximation solution are obtained in the form ofenergy norm and L2 -norm.