DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Johannes Pfefferer, GMU

**Title: ***
Finite element error estimates for semilinear elliptic Neumann
boundary control problems in polygonal domains
*

**Abstract:**
This talk is concerned with the discretization error analysis
for semilinear elliptic Neumann boundary control problems in polygonal
domains where the control has to fulfil pointwise inequality
constraints. In order to solve this problem the state and the adjoint
state are discretized by linear finite elements, whereas the control is
approximated by piecewise constant functions. In a postprocessing step
approximations of the continuous optimal control are constructed which
possess superconvergence properties, i.e., by imposing second order
sufficient optimality conditions it is possible to prove nearly second
order convergence for the postprocessed control on quasi-uniform meshes
in domains with largest interior angle smaller than 2pi/3. However,
for larger interior angles the presence of corner singularities lowers
the convergence rates in general. In that case mesh grading techniques
are used to compensate this negative influence. Finally, the quality of
the approximations is demonstrated by a numerical example.

**Time:** Friday, November 20, 2015, 1:30-2:30 p.m.

**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