Modified nonlocal boundary value problem method for an ill-posed problem for the biharmonic equation. (English) Zbl 1471.65178
Summary: In this paper, we propose a modified nonlocal boundary value problem method for an homogeneous biharmonic equation in a rectangular domain. We show that the considered problem is ill-posed in the sense of Hadamard, i.e. the solution does not depend continuously on the given data. Convergence estimates for the regularized solution are obtained under a priori bound assumptions for the exact solution. Some numerical results are given to show the effectiveness of the proposed method.
MSC:
| 65N20 | Numerical methods for ill-posed problems for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 31A30 | Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions |
| 35B45 | A priori estimates in context of PDEs |
| 35J40 | Boundary value problems for higher-order elliptic equations |
| 35R25 | Ill-posed problems for PDEs |
| 47A52 | Linear operators and ill-posed problems, regularization |
Keywords:
biharmonic equation; ill-posed problem; regularization method; convergence estimate; a priori estimatesReferences:
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