A Goal-Oriented Approach to Least-Squares Finite Element Methods
Date and time:
Tuesday, October 11, 2011 - 3:45pm
In this talk we introduce an approach that augments least-squares finite element formulations with user-specified goals or quantities-of-interest. The method incorporates the quantity-of-interest into the least squares functional and inherits the global approximation properties of the standard formulation as well as increased resolution of the goal. We establish theoretical properties such as optimality and enhanced convergence under a set of general assumptions. Moreover, we introduce an adaptive approach that results in efficient, adaptively refined approximations. Several numerical experiments for a range of situations are presented to highlight our methodology.