**Date & Time:** Thursday, October 11, 2012, 16:00-16:40.

**Venue:** Ramanujan Hall

**Title:**A posteriori error estimates for nonconforming finite
element methods for fourth-order problems on rectangles

**Speaker: ** Prof. Dietmar Gallistl

Humboldt-Universität zu Berlin

**Abstract:** The a posteriori error analysis of conforming finite element
discretisations of the biharmonic problem for plates is well
established, but nonconforming discretisations are more
easy to implement in practice. The a posteriori error analysis for the
Morley plate element appears very particular because two edge
contributions from an integration by parts vanish simultaneously. This miracle does not arise for popular
rectangular nonconforming finite element schemes like the nonconforming
rectangular Morley finite element, the incomplete biquadratic finite element, and the Adini finite element.
This talk introduces a novel methodology and utilises some conforming discrete space on macro
elements to prove reliability and efficiency of an explicit residual-based a
posteriori error estimator for two of these methods. An application to the Morley triangular finite
element shows the surprising result that all averaging techniques yield reliable error
bounds. Numerical experiments confirm the reliability and efficiency for the established a
posteriori error control on uniform and graded tensor-product meshes.