Wednesday, 12 February, 2014
SPEAKER: Prof. Xiaobing Feng, Math, UT
TITLE: Numerical Differential Calculus: A New Paradigm for Developing Numerical Methods for PDEs
ABSTRACT: In this talk I shall first present a newly developed (discontinuous Galerkin finite element) differential calculus theory for approximating weak (or distributional) derivatives of broken Sobolev functions. Various properties and calculus rules (such as product and chain rule, integration by parts formula and divergence theorem) for the proposed numerical derivatives will be presented. I shall then discuss how to use those numerical differential calculus machineries to systematically design numerical methods for various linear and nonlinear (including fully nonlinear) PDEs.