[Faculty] Fwd: [CSRC-SDSU COLLOQUIUM]: Combining Geometric Time and Mimetic Spatial Finite Difference Discretizations

[Jose Castillo]

*DATE*:  Friday, November 18th, 2016

*TITLE*: Combining Geometric Time and Mimetic Spatial Finite Difference
Discretizations.

*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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Jose E. Castillo  Ph.D.

Director / Professor

Computational Science Research Center

5500 Campanile Dr

San Diego State University

San Diego CA 92182-1245

619 5947205/3430, Fax 619-594-2459

 http://www.csrc.sdsu.edu/mimetic-book/
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