Séminaire Martin Halla (Max Planck Institute for Solar System Research)
In the 1970s Stummel initiated the study of ``discrete approximation schemes'', which is a very generic framework to conduct the convergence analysis of numerical methods for e.g. source problems, holomorphic eigenvalue problems, nonlinear problems, etc.. In this context a most important property is the regularity of approximations. However, until recently this framework was only applied to weakly coercive problems for which the regularity of Galerkin approximations is easy to obtain.
In the last two decades the notion of weak T-coercivity became popular to study the well-posedness (Fredholmness) of all kinds of partial differential equations, e.g. Maxwells equations, interior transmission eigenvalue problems, dispersive transmission problems and Galbruns equation.
In this talk I present a technique to mimic the weak T-coercivity analysis on the discrete level to obtain the regularity and hence convergence of approximations. I present the application to Maxwells equations and Galbruns equation.