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 |