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Approximate solution of inverse problem for elliptic equation with overdetermination. (English) Zbl 1291.65328

Summary: A finite difference method for the approximate solution of the inverse problem for the multidimensional elliptic equation with overdetermination is applied. Stability and coercive stability estimates of the first and second orders of accuracy difference schemes for this problem are established. The algorithm for approximate solution is tested in a two-dimensional inverse problem.

MSC:

65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
35R30 Inverse problems for PDEs
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