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April 2018

Jared Wunsch, Northwestern University – Analysis & PDE Seminar

April 25 @ 4:00 pm - 5:00 pm

Title: Diffraction of semiclassical singularities by conormal potentials. Abstract: Consider a semiclassical Schr\"odinger operator $P=h^2\Delta+V-E,$ where $V$ has a conormal singularity along a hypersurface.  The singular structure of $V$ affects the propagation of semiclassical singularities for solutions to $Pu=0,$ and in particular there is a `diffraction' of wavefront set by the interface: singularities are reflected as well as transmitted as they cross the interface transversely.  The reflected wave, however, is more regular, with the improvement depending on the regularity of the interface. …

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Tobin Isaac, Georgia Tech – Applied Mathematics Colloquium

April 27 @ 4:00 pm - 5:00 pm

Title: Mixed Finite Element Extensions of MAC Schemes Abstract: The Marker-and-Cell (MAC) discretization is a surprisingly efficient discretization for Stokes equations, converging at second order with a small number of degrees of freedom and sparse stencil.  But that second order convergence can be explained by a cancellation of errors, which makes it fragile.  Can we maintain second order convergence for MAC discretizations on deformed or non-conforming grids, or for creeping flows with anisotropic effective viscosities?  We develop an approach for…

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