Stable and Unstable Discretization of Partial Differential Equations

30 January 2004
16:30
Doug Arnold
Abstract
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.