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Research and Discovery | Research Events

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October 15, 2019 | 1:00 p.m. - 2:00 p.m.
Category: Seminar
Location: Faculty/Administration #1140 | Map
656 W. Kirby
Detroit, MI 48202
Cost: Free

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.

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