A filter method with a priori and a posteriori parameter choice for the regularization of Cauchy problems for biharmonic equations
A filter method with a priori and a posteriori parameter choice for the regularization of Cauchy problems for biharmonic equations
Source title:
Numerical Algorithms, 86: 1721-1746,
2020
(ISI)
Academic year of acceptance:
2020-2021
Abstract:
In the present paper, we devote our effort to Cauchy boundary value problems for biharmonic equations. In general, the investigated problem is ill-posed. Therefore, we develop a filter method to defeat the ill-posedness of the problem. Explicit convergence rate is established under both a priori and a posteriori parameter choice rules. Finally, a numerical example is presented to illustrate the ill-posedness of the problem as well as the effectiveness of the proposed method.