TY - JOUR
T1 - Convergence Estimates for Some Regularization Methods to Solve a Cauchy Problem of the Laplace Equation
AU - T. Wei, H. H. Qin & H. W. Zhang
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 459
EP - 477
PY - 2011
DA - 2011/04
SN - 4
DO - http://doi.org/10.4208/nmtma.2011.m1015
UR - https://global-sci.org/intro/article_detail/nmtma/5978.html
KW - Cauchy problem, Laplace equation, regularization methods, convergence estimates.
AB - <p style="text-align: justify;">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.</p>