An Extended Finite Element Method For The Elasticity Interface Problem

In the thesis,we propose an extended finite element method for elasticity interface problems,and present optimal a priori error estimate and the estimates of the con-dition number of the discrete system of equation.The method proposed is verified by numerical experiments.We start with elasticity interface problems with a mixed form,and introduce the extended finite element method for the problem.By introducing a ghost penalty stabilization,we proved the well-posedness of the method which is independent of the location of the interface;Next,we present the analysis of boundedness and coercivity,which is necessary in the proof of the existence and uniqueness of the solution.At the same time,we also get the optimal a priori error estimate.Then,we show that the condition number of stiffness matrix is O(h-2)independent of the location of the interface.