Applied Mathematics Seminar - Constantin Bacuta
This event is in the past.
Detroit, MI 48202
Speaker: Constantin Bacuta, University of Delaware
Title: Least Squares Discretization of Mixed Variational Problems
Abstract: We introduce a new least squares method for discretizing boundary value problems written as mixed variational formulations. At the continuous level we assume a stability LBB condition and data compatibility. The proposed discretization method is associated with standard discretization of an equivalent saddle point reformulation of the original mixed problem. Choices for the discrete spaces can be done such that a discrete $inf-sup$ condition is automatically satisfied. We choose a standard conforming test spaces first. A corresponding trial spaces is chosen second by using the action of the continuous operator that defines the mixed problem. The implementation of the proposed iterative process does not require nodal bases for the trial space. A natural preconditioning strategy based on the general theory of preconditioning symmetric problems is proposed. Applications of the method include discretizations of first order systems of parametric PDEs, such as the time-hamonic Maxwell equations and second order PDEs with variable or discontinuous coefficients.