Scientific Computing Group Seminars - Detail View

Speaker: A. Patera

Affiliation: Mechanical Engineering, MIT

Talk Title: Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations

Invited by: George Karniadakis

Time: Dec. 05 2008 11 a.m.

Location: 182 George Street, Room 110

Abstract:

We discuss reduced basis approximation and associated a posteriori error estimation for reliable real-time solution of parametrized partial differential equations. The crucial ingredients are rapidly convergent Galerkin approximations over a space spanned by “snapshots” on the parametrically induced solution manifold; effective constructions for stability-constant lower bounds; rigorous and sharp a posteriori error estimators for the outputs/quantities of interest; efficient Greedy (in parameter) or POD (in time) Greedy (in parameter) selection of quasi-optimal samples; and Offline-Online computational procedures for rapid calculation in the many-query and real-time contexts. We consider linear and nonlinear elliptic problems, linear and nonlinear parabolic equations, and linear hyperbolic equations. Examples are drawn from heat transfer (steady and unsteady conduction and convection), solid mechanics (e.g., crack stress intensity factors), and fluid dynamics (the incompressible Navier-Stokes equations and Boussinesq natural convection).