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RWTH Publication No: 442964 2014   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.
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KEYWORDS |
reduced basis method, model order reduction, parametrized partial differential equations, a posteriori error estimation, nonlinear diffusion equation
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CORRESPONDING AUTHOR |
Martin Grepl, +49 241 8096470, Fax: +49 241 80696470, Email: grepl@igpm.rwth-aachen.de |