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D. Praetorius, P. Wissgott:
"A Space-Time Adaptive Algorithm for Linear Parabolic Problems";
Poster: Einsteins in the City 2 International Student Research Conference, New York; 10-30-2007 - 10-31-2007.

We present a space-time adaptive algorithm for the numerical solution
of linear parabolic equations. The algorithm is mathematically based
on a residual-based a posteriori error estimate which yields an upper
and lower bound for the error in the space-time energy norm. Our
analysis extends a recent work of Verfürth (2005) from space-time
constant coefficients to the case of space-time dependent
coefficients. This error estimate provides the mathematical basis for
reliable and efficient numerical simulations. In particular, it
provides a mean to control and choose the time step size as well as
the spatial mesh size automatically. By others, the spatial mesh may
be refined and/or coarsened for two consecutive time steps.

The presentation consists of 4 parts: First, the problem statement
and examples of technical problems that can be treated by the
developed software. Second, the presentation and discussion of the
derived a posteriori error estimate. Third, the flow chart of the
adaptive algorithm. Finally, numerical experiments like the
propagation of a pollution in groundwater flow.

(The contribution was awarded by the Einsteins in the City Poster Award 2007.)