Return to Colloquia & Seminar listing
Adaptive Mollifiers -- High Resolution Recovery of Piecewise Smooth Data from its Spectral Information
Applied Math| Speaker: | Jared Tanner, UC Davis |
| Location: | 693 Kerr |
| Start time: | Fri, Oct 4 2002, 4:10PM |
Description
Spectral projections enjoy high order convergence for globally
smooth functions. However, a single discontinuity introduces O(1) spurious
oscillations, Gibbs' Phenomena, and reduces the high order convergence rate
to first order. We will show how adaptive mollifiers can be used to recover
the high order convergence rate as well as remove the spurious oscillations
found near a discontinuity. In addition, when these adaptive mollifiers are
applied to an equidistant sampling of piecewise smooth functions we obtain
an exponentially accurate "interpolation" scheme. This is a powerful new
tool for equidistant data with applications in image processing and non-linear
conservation laws. Time permitting, applications to scalar hyperbolic
conservation laws will be shown.
This research was conducted jointly with Eitan Tadmor.