Convergence Estimates for Some Regularization Methods to Solve a Cauchy Problem of the Laplace Equation

摘要

In this paper,we give a general proof on convergence estimates for some regularization methods to solve a Cauchy problem for the Laplace equation in a rectangular domain.The regularization methods we considered are: a non-local boundary value problem method,a boundary Tikhonov regularization method and a generalized method.Based on the conditional stability estimates,the convergence estimates for various regularization methods are easily obtained under the simple verifications of some conditions.Numerical results for one example show that the proposed numerical methods are effective and stable.