Past Forthcoming Seminars

2 February 2004
Daniel Faraco
Recently Friesecke, James and Muller established the following quantitative version of the rigidity of SO(n) the group of special orthogonal matrices. Let U be a bounded Lipschitz domain. Then there exists a constant C(U) such that for any mapping v in the L2-Sobelev space the L^2-distance of the gradient controlls the distance of v a a single roation. This interesting inequality is fundamental in several problems concerning dimension reduction in nonlinear elasticity. In this talk, we will present a joint work with Muller and Zhong where we investigate an analagous quantitative estimate where we replace SO(n) by an arbitrary smooth, compact and SO(n) invariant subset of the conformal matrices E. The main novelty is that exact solutions to the differential inclusion Df(x) in E a.e.x in U are not necessarily affine mappings.
  • Applied Analysis and Mechanics Seminar
30 January 2004
Doug Arnold
Stability is central to the study of numerical algorithms for solving partial differential equations. But stability can be subtle and elusive. In fact, for a number of important classes of PDE problems, no one has yet succeeded in devising stable numerical methods. In developing our understanding of stability and instability, a wide range of mathematical ideas--with origins as diverse as functional analysis,differential geometry, and algebraic topology--have been enlisted and developed. The talk will explore the concept of stability of discretizations to PDE, its significance, and recent advances in its understanding.