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A mixed least-squares method for an inverse problem of a nonlinear beam equation. (English) Zbl 0928.74101

Summary: We discuss a finite element method based on the mixed least-squares formulation. The cost functional turns out to be a polynomial, so that its gradient and Hessian can be computed efficiently. A multi-level Newton iteration is introduced for minimizing the cost functional that can converge from a rough initial guess. We derive error estimates which not only are optimal in a certain configuration, but also supply rules for choosing regularization parameters according to the mesh size and the random noise in the data.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
34A55 Inverse problems involving ordinary differential equations
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