Numerical Analysis Seminar
Speaker: Prof. Carsten Carstensen
Host: Neela Nataraj
Title: Computation of Plates
Time, day and date: 3:00:00 PM, Wednesday, March 12
Venue: Ramanujan Hall
Abstract: The general and short title might be better specified and then stands for the mathematical foundation of the adaptive computation of plates or simply the numerical treatment of the biharmonic equation with conforming and nonconforming schemes. In the spirit of John H. Argyris (1913-2004) the complicated conforming finite element scheme marks the beginning of the finite element area with a straightforward mathematics and an involved implementation.
The presentation discusses the simplest lowest-order nonconforming finite element schemes with an easy implementation and a more involved mathematics. In fact, 30 lines of Matlab suffice in a program for basic Morley finite element simulations.
The talk concerns a larger class of popular (piecewise) quadratic schemes for the fourth-order plate bending problems based on triangles are the nonconforming Morley finite element, two discontinuous Galerkin, the C0 interior penalty, and the WOPSIP schemes. The first part of the presentation discusses recent applications to the linear bi-Laplacian and to semi-linear fourth-order problems like the stream function vorticity formulation of incompressible 2D Navier-Stokes problem and the von Karman plate bending problem. The role of a smoother is emphasised and reliable and efficient a posteriori error estimators give rise to adaptive mesh-refining strategies that recover optimal rates in numerical experiments. The last part addresses recent developments on adaptive multilevel Argyris finite element methods. The presentation is based on joint work with B. Grass le (University of Zurich) and N. Nataraj (IITB in Mumbai) partly reflected in the references below.
The eye-catcher is a photo from the Monash campus and illustrates that the plate simulation may fail because of interactions with other loadings and
related to simulations in [8].