A C0 finite element method for an inverse problem

摘要

A C0 finite element method is presented for an inverse problem in which the coefficient in the differential operator is to be determined from the measurement of the solution of a boundary value problem. The unknown in the inverse problem is approximated by a minimizer of a cost function that includes both the output error and equation error. Error estimates in a weighted H−1 norm and L2 are given. Numerical examples are presented to show features of the method.