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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Numerical Analysis Seminars: Elliptic Reconstruction in A Posteriori Error Analysis for Evolution Equations

Presented by Omar Lakkis, University of Sussex

18 January 2008 14:15 in eScience 034

I will address the usage of the elliptic reconstruction technique
(ERT) in a posteriori error analysis for fully discrete schemes for
evolution partial differential equations with particular focus on
parabolic equations. A posteriori error estimates are effective tools
in error control and adaptivity and a mathematical rigorous derivation
justifies and improves their use in practical implementations.

The flexibility of the ERT allows a virtually indiscriminate use of
various parabolic PDE techniques such as energy methods, duality
methods and heat-kernel estimates, as opposed to direct approaches
which leave less maneuver room. Thanks to the ERT, parabolic stability
techniques can be combined with different elliptic a posteriori
analysis techniques, such as residual or recovery estimators, to
derive a posteriori error bounds. The method unifies and simplifies
most previously known analysis, and it provides previously unknown
error bounds (e.g., pointwise norm error bounds for the heat
equation). [Results with Ch. Makridakis and A. Demlow.]

A further feature of the ERT, which I would like to highlight, of the
ERT is its simplifying power. It allows to derive estimates where the
analysis would be dautingly complicated. As an example, I will
illustrate its use in the context of non-conforming methods, with a
special eye on discontinuous Galerkin methods [with E. Georgoulis]
and "ZZ" recovery-type estimators [with T. Pryer].

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