A finite element method for an ill-posed problem Original Research Article

For an ill-posed problem which has its origin in several applications (e.g. electrocardiology) a weak formulation is given over a Hilbert space without any constraints. This is achieved by means of Lagrangian multipliers. Beside theoretical questions (e.g. existence and uniqueness of a solution) a finite element approximation is considered. Error estimates, an investigation of the condition number of the corresponding finite-dimensional system and a numerical example are given.