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In this paper, we are concerned with the identification of the piecewise constant Robin coefficient in an elliptic equation. The iterative regularization method is one of the very effective methods for solving this kind of nonlinear ill-posed inverse problems. But it usually requires to solve numerous amounts of forward solutions during the iterative process, which will cost a lot of computational time in high-dimensional spaces. A reduced basis method is considered to reduce the computational time for solving the forward problems, and its error estimate is also studied. Finally, we propose a reduced basis Landweber algorithm to solve the elliptic inverse Robin problem and present several numerical experiments to demonstrate the accuracy and efficiency of the algorithm.

A reduced basis Landweber method for the identification of piecewise constant Robin coefficient in an elliptic equation