Prof. Carsten Carstensen

Contact: Friederike Hellwig (hellwigf@math.hu-berlin.de)

Humboldt-Universität zu Berlin, Institut für Mathematik

Rudower Chaussee 25, 12489 Berlin

Room 2.417

April 19, 2017 | 09:15 | Joscha Gedicke, Universität Wien |
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»An adaptive finite element method for two-dimensional Maxwell's equations« (Abstract) | ||

April 26, 2017 | 09:15 | Johannes Storn, HU Berlin |

»Asymptotic Exactness of the Least-Squares Finite Element Residual« | ||

May 3, 2017 | 09:15 | Georgi Mitsov, HU Berlin |

»Discrete Gronwall-type estimates for a family of discontinuous Petrov-Galerkin methods for the time-dependent Maxwell equations, Part I« | ||

May 9, 2017 | 14:00 | Georgi Mitsov, HU Berlin |

»Discrete Gronwall-type estimates for a family of discontinuous Petrov-Galerkin methods for the time-dependent Maxwell equations, Part II« | ||

May 10, 2017 | 09:15 | Nando Farchmin, HU Berlin |

»Analysis of a dPG FEM for Optimal Material Design« | ||

May 16, 2017 | 14:00 | Georgi Mitsov, HU Berlin |

»Discrete Gronwall-type estimates for a family of discontinuous Petrov-Galerkin methods for the time-dependent Maxwell equations, Part III« | ||

May 17, 2017 | 09:15 | Lukas Gehring, HU Berlin |

»Die Konstante in dem Satz von Binev-Dahmen-DeVore (über die Gesamtzahl von Dreiecken bei AFEM)« | ||

May 31, 2017 | 09:15 | Philipp Bringmann, HU Berlin |

»Rate optimal adaptive least-squares finite element scheme for the Stokes equations« | ||

June 14, 2017 | 09:15 | Stephan Schwöbel, HU Berlin |

»Übertragung einer dPG-Methode in eine Least Squares Methode« | ||

June 21, 2017 | 09:15 | Lukas Gehring, HU Berlin |

»Die Konstante in dem Satz von Binev-Dahmen-DeVore, Teil II« | ||

June 28, 2017 | 09:15 | Andreas Veeser, University of Milan |

»Quasi-optimality in parabolic spatial semidiscretizations« (Abstract) | ||

July 11, 2017 | 13:30 | Friederike Hellwig, HU Berlin |

»Nonlinear Discontinuous Petrov-Galerkin Methods« | ||

July 18, 2017 | 13:30 | Philipp Bringmann, HU Berlin |

»Quasi-interpolation operators for Nédélec functions - A short review« | ||

July 18, 2017 | 14:00 | Johannes Storn, HU Berlin |

»Asymptotic Exactness of the Least-Squares Finite Element Residual, Part II« |

We extend the Hodge decomposition approach for the cavity problem of two-dimensional time harmonic Maxwell's equations to include the impedance boundary condition, with anisotropic electric permittivity and sign changing magnetic permeability. We derive error estimates for a P_{1} finite element method based on the Hodge decomposition approach and develop a residual type a posteriori error estimator. We show that adaptive mesh refinement leads empirically to smaller errors than uniform mesh refinement for numerical experiments that involve metamaterials and electromagnetic cloaking. The well-posedness of the cavity problem when both electric permittivity and magnetic permeability can change sign is also discussed and verified for the numerical approximation of a flat lens experiment.

We analyze the interplay of the time derivative and the spatial
discretization of parabolic initial-boundary value problems. Addressing
time-independent and time-dependent spatial discretizations, our focus
is on quasi-optimality and best error localization. Best error
localization means that the best error over the whole domain is
equivalent to an l_{2}-norm of best errors over small subdomains, which
ideally are mesh elements. The key tool for quasi-optimality is the
inf-sup theory, with a formula for the quasi-optimality constant which
is of independent interest.