Error Analysis for Reduced Order Models of Nonlinear Partial Differential Equations

Dr. Sivaguru S. Ravindran

Department of Mathematical Sciences
UAHuntsville

5 February 2010
218 Shelby Center
3:00 (Refreshements at 2:30)

Abstract

Model reduction has become an active area of scientific and engineering research due to its ability to reduce the complexity of dynamical systems to enable numerical simulation, optimization and control design. The past decade has seen significant progress in development and analysis of model reduction techniques. Proper orthogonal decomposition (POD) and numerical linear algebra have played a crucial role in these developments. Despite these developments, many issues remain to be solved including error analysis and techniques for nonlinear parameterized dynamical systems.

In this talk, we will discuss error analysis for reduced order models of nonlinear PDEs using discrete energy estimates. Within the talk several numerical examples will illustrate the use of POD reduced order models in the context of simulation and control of nonlinear PDEs.