Identification of transmissivity coefficients by mollification techniques. Part II: n-dimensional elliptic problems

We analyze the numerical identification of the transmissivity coefficient in the n-dimensional model for linear elliptic equations. This problem arises in a number of important practical problems in science. The identification of this coefficient is an inverse problem which is highly ill-posed and difficult to solve. In order to address the ill-posedness of this parameter estimation problem, we use mollification techniques combined with finite differences to get a numerical method which is easy to implement in rectangular domains. Some numerical examples of interest for n = 2 are presented.