Kolloquiumsvortrag: Prof. Dr. Ralf Hiptmair, ETH Zürich / 29.01.2016

29.01.2016 von 14:15 bis 15:45

Institut für Informatik, Ludewig-Meyn-Str. 2, 24118 Kiel, Übungsraum 2

Titel:  Maxwell and the Hodge Laplacian


The linear Maxwell equations in frequency domain can be recast in several dierent forms,
as rst-order system, as second-order equation involving the double-curl operator, or a
second-order equation featuring the Hodge-Laplacian 􀀀 := curl curl􀀀grad div.
Variational equations or boundary integral equations arising from these dierent formulations
are equivalent, but pose very dierent challenges when it comes to discretization.
For instance, there is the startling failure of smooth functions to be dense in
H0(curl; ) \H(div; ) for certain domains . This foils direct Galerkin discretization
of the Hodge-Laplacian and enforces the use of a mixed approach.
Similarly, rst-kind boundary integral operators associated with u = 0 display a strange
lack of coercivity. The culprit is the failure of certain combinations of boundary conditions
for to ensure uniqueness of solutions of the related boundary value problems.

Prof. Börm

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