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Error analysis of an equation error method for the identification of the diffusion coefficient in a quasi-linear parabolic differential equation. (English) Zbl 0928.35198

Summary: We consider the inverse problem of reconstructing the diffusion coefficient in a quasi-linear parabolic differential equation in divergence form from measurements of the solution at a finite number of points in the interior of the domain. An equation error method is developed which transforms the inverse problem into a system of linear operator equations for the diffusion coefficient and which can be solved by the conjugate gradient method in a very efficient and stable manner. A detailed error analysis relates the required number of measurements with their accuracy. Numerical results illustrate the performance of the method.

MSC:

35R30 Inverse problems for PDEs
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
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