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Cheng, Hao; Feng, Xiao-Li; Fu, Chu-Li

A mollification regularization method for the Cauchy problem of an elliptic equation in a multi-dimensional case. (English) Zbl 1206.65224

Inverse Probl. Sci. Eng. 18, No. 7, 971-982 (2010).
A Cauchy problem for an elliptic equation is considered. This problem is ill-posed since the solution, if it exists, does not depend continuously on the data. The considered ill-posed problem is replaced by a problem with mollified data and some error estimates between the solutions of the two problems are established. Moreover, some numerical experiments are presented to verify the proposed regularization method.
Reviewer: Ruxandra Stavre (Bucureşti)

Cited in 9 Documents

MSC:

65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
35R25 Ill-posed problems for PDEs
35J25 Boundary value problems for second-order elliptic equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs

Keywords:

elliptic equation; Cauchy problem; ill-posed problem; mollification method; error estimates; numerical experiments; regularization method
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\textit{H. Cheng} et al., Inverse Probl. Sci. Eng. 18, No. 7, 971--982 (2010; Zbl 1206.65224)
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