WFU Physics Colloquium

TITLE: Barrier methods for critical exponent problems in general relativity

SPEAKER: Professor Jennifer B. Erway,

TIME: Wednesday February 8, 2012 at 4:00 PM

PLACE: Room 101 Olin Physical Laboratory

Abstract: In this talk we consider numerical methods for approximating positive solutions to nonlinear geometric elliptic partial differential equations containing critical exponents. This class of problems includes the Yamabe problem and the Einstein constraint equations in general relativity. These problems may exhibit multiple solutions, although only positive solutions typically have meaning. This creates additional complexities in both the theory and numerical treatment of such problems, as this feature introduces both non-uniqueness as well as the need to incorporate an inequality constraint into the formulation. This talk focuses on numerical methods based on a finite element method together with a barrier method from nonconvex optimization to handle the inequality constraint. The talk will begin with an overview of weak formulations, weak solutions, energy functionals, finite element methods, and barrier methods. Numerical results will be presented.