BEGIN:VCALENDAR
VERSION:2.0
PRODID:Baylor CMS Calendar /PHP/
METHOD:PUBLISH
BEGIN:VTIMEZONE
TZID:US_Central
BEGIN:STANDARD
DTSTART:20001029T020000
RRULE:FREQ=YEARLY;WKST=MO;INTERVAL=1;BYMONTH=11;BYDAY=1SU
TZNAME:Standard Time
TZOFFSETFROM:-0500
TZOFFSETTO:-0600
END:STANDARD
BEGIN:DAYLIGHT
DTSTART:20010401T020000
RRULE:FREQ=YEARLY;WKST=MO;INTERVAL=1;BYMONTH=3;BYDAY=2SU
TZNAME:Daylight Saving Time
TZOFFSETFROM:-0600
TZOFFSETTO:-0500
END:DAYLIGHT
END:VTIMEZONE
BEGIN:VEVENT
UID:Baylor_CMS_Event-111696
DTSTAMP:20210305T172205Z
SUMMARY:Mathematics Colloquium - A Lagrangian Scheme for the Solution of Nonlinear Diffusion Equations
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:=0D=0A=
Mathematics ColloquiumJointly with CASPER=0D=0A=
=0D=0A=
=0D=0A=
Professor Bertram Düring=0D=0A=
Department of Mathematics=0D=0A=
University of Sussex=0D=0A=
=0D=0A=
=0D=0A=
Topic: A Lagrangian Scheme for the Solution of Nonlinear Diffusion Equations=0D=0A=
=0D=0A=
=0D=0A=
Refreshments: 1:30 pm in Room 318 Sid Richardson=0D=0A=
=0D=0A=
=0D=0A=
Abstract: Nonlinear diffusion equations whose dynamics are driven by internal energies and given external potentials, e.g., the porous medium equation and the fast diffusion equation, have received a lot of interest in mathematical research and practical applications alike in recent years. Many of them have been interpreted as gradient flows with respect to some metric structure. When it comes to solving partial differential equations of gradient flow type numerically, it is natural to ask for appropriate schemes that preserve the equations' special structure at the discrete level.=0D=0A=
=0D=0A=
=0D=0A=
In this talk we present a Lagrangian numerical scheme for solving nonlinear degenerate Fokker-Planck equations in multiple space dimensions. The scheme applies to a large class of nonlinear diffusion equations. The key ingredient in our approach is the gradient flow structure of the dynamics. For discretization of the Lagrangian map, we use a finite subspace of linear maps in space and a variational form of the implicit Euler method in time. Thanks to that time discretization, the fully discrete solution inherits energy estimates from the original gradient flow, and these lead to weak compactness of the trajectories in the continuous limit. We discuss the consistency of the scheme in two space dimensions and present numerical experiments for the porous medium equation.=0D=0A=
=0D=0A=
LOCATION:Room 207 Sid Richardson Building
DTSTART;TZID=US_Central:20171205T140000
DTEND;TZID=US_Central:20171205T150000
END:VEVENT
END:VCALENDAR