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Preprint-No.: <   401   >   Published in: July 2014   PDF-File: IGPM401.pdf
Title:A Certified Reduced Basis Method for Parametrized Quadratically Nonlinear Diffusion Equations
Authors:Mohammad Rasty, Martin Grepl
Abstract:
We present a certified reduced basis method for a steady-state quadratically nonlinear diffusion equation. We employ the standard Galerkin recipe for the reduced basis approximation and derive associated a posteriori error estimation procedures based on the Brezzi-Rappaz-Raviart (BRR) framework. We show that all necessary ingredients, i.e., the dual norm of the residual, the Sobolev embedding constant, and a lower bound of the inf-sup constant, can be decomposed in an offline-online computational decompostion. Numerical results are presented to confirm the rapid convergence of the reduced basis approximation and the rigor and sharpness of the associated a posteriori error bound.
Keywords:reduced basis method, model order reduction, parametrized partial differential equations, a posteriori error estimation, nonlinear diffusion equation
Corresponding author:Martin Grepl, +49 241 8096470, Fax: +49 241 80696470, Email: grepl@igpm.rwth-aachen.de