Stable and Unstable Discretization of Partial Differential Equations

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.