Numerical Method With The Boltzmann Boundary Conditions For Elliptic Problems

In this paper,we discussed the numerical methods for the elliptic problem with nonlinear Boltzmann boundary conditions.In chapter 1,the upper-lower solution method for elliptic problems is introduced:one is the Picard iteration method and another is the Newton iteration method.We prove that the Picard iteration is linear convergent and the Newton scheme is of second order convergence rate,the numerical results confirm the theoretical analysis.In chapter 2,two domain decomposition methods are discussed,a multiplicative and an addictive domain decomposition methods are used to solve the the coupled system,the numerical experiments show the convergence of the two methods.Chapter 3 is mainly dealt with the Stefan inverse problem.Firstly the inverse problem for the nonlinear boundary problem is proposed,by shape analysis method we extend the conclusion for problem with linear boundary conditions to nonlinear ones,the velocity in the level set method is chosen to reduce the residual norm.