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
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Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491