Combining Geometric Time and Mimetic Spatial Finite Difference Discretizations.
TITLE:
Combining Geometric Time and Mimetic Spatial Finite Difference
Discretizations.
DATE:
Friday, November 18th, 2016
TIME:
3:30 PM
LOCATION:
GMCS 314
SPEAKER:
Dr. Stanly Steinberg, Professor of Mathematics, University of New
Mexico.
ABSTRACT:
Geometric time and mimetic spatial discretization have recently
undergone, INDEPENDENTLY, rapid development. Unfortunately
when these discretization are combined some of the advantages of
the individual algorithms are typically lost. In this talk I will
present some ideas on how to overcome such problems. There will
be a workshop on this topic next summer:
http://www.birs.ca/events/2017/5-day-workshops/17w5152
The Lax equivalence theorem for finite difference methods for the
numerical solution of partial differential equations states that
a discretization is convergent if and only if it is consistent and
stable (1956). There are similar results for finite elements that
involve the inf-sup condition. For some problems with these
ideas see the slides at
http://www.math.umn.edu/~arnold/talks/feng-kang-print.pdf
An important problem is that convergence is not enough to guarantee
that a model is accurately representing a physical problem.
The goal of the integration of the time and spatial discretization
methods is to, of course, have accuracy and stability and thus
convergence, but also to preserve additional important properties
of the continuum models such as conservation of mass and energy
and the divergence of the electric and magnetic fields being zero
when there are no sources.
HOST:
Dr. Jose Castillo
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