DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**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

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491