Data completion for linear symmetric operators as a Cauchy problem: An efficient method via energy-like error minimization

Abstract

Data completion is a problem in which known or measured superabundant data exist for part of the boundaries of a domain, whereas the data for the rest of the boundaries are unknown. Thus the aim is to determine the solution of a known PDE defined throughout the domain, which satisfies the superabundant data and then identifies the missing ones. For linear symmetric operators, we propose a general method to solve the data completion problem as a Cauchy problem. Various applications are described for stationary conduction and elastostatic problems.