Applied and Computational Math Seminar: Best approximation of the Galerkin solution for elliptic and parabolic problems in L-infinity.

Speaker:Dmitriy Leykekhman, University of Connecticut
Title: Best approximation of the Galerkin solution for elliptic and parabolic problems in L-infinity.

Abstract: Finite element error analysis of state constrained optimal control problem or optimal control problems with pointwise controls often requires error estimates in form of the best approximation due to low regularity of the optimal state or adjoint variable. Such best approximation error estimates are well known for elliptic problems. For the parabolic problems such results are mainly available for the semidiscrete solutions. In my talk, after reviewing best approximation properties for elliptic problems, I will show how the global and local best approximation results follow from our recently established results on discrete maximal parabolic regularity for a family of discontinuous Galerkin time discretization methods and the stability of the Ritz projection in L-infinity norm.

Time: Friday, November 17, 2017, 1:30-2:30pm

Place: Exploratory Hall, Room 4106