• Dr. Serge Prudhomme
  • Institute for Computational Engineering and Sciences (ICES)
  • 113 McBryde Hall
  • 4:00 p.m.
  • Faculty Host: Dr. Christopher Roy

Finite Element methods are widely used today for the solution of boundary- and initial-value problems of scientific and engineering interest. However, these methods, as with any other numerical methods, only provide approximations of the true solutions, which, therefore, inevitably contain errors due to the discretizations in space and time. In this talk, we will describe in detail adjoint-based techniques for a posteriori estimation and adaptive control of the discretization errors, measured with respect to quantities of interest. These so-called goal-oriented error estimation methods will be illustrated on a series of model examples, ranging from linear elliptic problems to nonlinear and time-dependent problems. We will also show how one can extend these methods to the case of coupled problems and how one can design adaptive methods for optimal control of the discretization error in the quantities of interest.