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SUMMARY:Finite element discretizations for nonlinear Schrödinger equation
 s with rough potentials
DTSTART:20181101T161500
DTEND:20181101T171500
DTSTAMP:20260407T020853Z
UID:09cd922e24957834bffd5dc65d0dd62da2426bcc3cb18f5ca51347f3
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Patrick Henning\, KTH\nIn this talk we consider the nume
 rical solution of a class of non-linear Schrödinger equations by Galerkin
  finite elements in space and a mass- and energy conserving variant of the
  Crank-Nicolson method in time. The usage of finite elements becomes neces
 sary if the equation contains terms that dramatically reduce the overall r
 egularity of the exact solution. Examples of such terms are rough potentia
 ls or disorder potentials as appearing in many physical applications. We p
 resent some analytical results that show how the reduced regularity of the
  exact solution could affect the expected convergence rates and how it res
 ults in possible coupling conditions between the spatial mesh size and the
  time step size. We will also demonstrate the significant importance of nu
 merical energy-conservation in applications with low-regularity by simulat
 ing the phase transition of a Mott insulator into a superfluid.
LOCATION:MA A1 10 https://plan.epfl.ch/?room=MAA110
STATUS:CONFIRMED
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