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Dr. Omar Lakkis (University of Sussex)
| Speaker: |
Dr. Omar Lakkis (University
of Sussex)
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| Date: |
Wednesday March 24, 2010
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| Title: |
Reconstructive aposteriori analysis and error control for
heat and wave equations
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Abstract
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Solution to
time-evolution partial differential equation (PDE) problems, such as
the (maybe nonlinear) diffusion equation or wave equation, can be
numerically simulated by a wide and reasonably understood class of
Galerkin methods, such as continuous/discontinuous finite elements.
On the other hand, error control and adaptive algorithms for such these
PDE's are still the object of intense research. In spite of many
achievements in this area since the early nineties, both the theory and
the practice for error control based adaptive methods to solve
stationary PDE's is much richer than its evolution counterpart.
In this talk, I will give an overview of the evolution background and
show how to take as big an advantage from the stationary theory in
order to analyse the error control evolution algorithms. The main tool
for this approach is Reconstructive Aposteriori Analysis, introduced in
the early noughties by Makridakis & Nochetto (2003) and further
developed by Akrivis, Makridakis, myself, Demlow, Pryer and Georgoulis
throughout the noughties.
I will address mostly my recent work (joint with Makridakis and
Georgoulis) on the wave equation and, time allowing, show recent
reconstructive applications by other researchers.
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