On Numerical Problems Caused by Discontinuities in Controls [chapter]

Christian Großmann, Antje Noack, Reiner Vanselow
2003 IFIP Advances in Information and Communication Technology  
The regularity of solutions of parabolic initial-boundary value problems directly depends upon the regularity of the boundary data. Reduced regularity of boundary data arise e.g. in optimal boundary control problems governed by evolution equations by a discretization of the control by piecewise constant functions and results in refined grids if automatic step size procedures in time are applied. In the present study effects to numerical methods for solving the state equations are illustrated.
more » ... reover, an appropriate splitting of the solution is used to improve the numerical behavior of the discretization technique as weil as of the optimization method applied to the control problern itself.
doi:10.1007/978-0-387-35699-0_14 fatcat:mgeucde3unc75cvvmnq2t3ypxm