FICTITIOUS DOMAINS METHODS WITH DISTRIBUTED LAGRANGE MULTIPLIERS PART I: APPLICATION TO THE SOLUTION OF ELLIPTIC STATE PROBLEMS

Abstract

Fictitious domain approaches are an attractive way to overcome the usual drawbacks of the so-called boundary variation technique for solving optimal shape problems. In the first part of this paper, we introduce fictitious domain methods with distributed Lagrange multipliers for elliptic state problems. Continuous formulations as well as their finite element discretizations are discussed. The second part of the paper will be devoted to the application of these methods to shape optimization.