|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|
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: firstname.lastname@example.org|