Graduate Seminar "Aktuelle Themen der Numerik"

Thursday, Feb 06, 2014, 02:00 pm

RB method for Nonlinear Evolutionary Diffusion Equations

Mohammad Rasty (IGPM, RWTH Aachen)

We present reduced basis approximation and associated "a posteriori" error estimation procedure for a steady-state and a time-dependent quadratically nonlinear diffusion equation. Certified reduced basis method has been developed previously for a large class of linear and nonlinear parametrized partial differential equations. Here we extend the methodology to treat quadratically nonlinear diffusion equations with two essential ingredients:
(i)  using the BRR framework to derive a sharp and rigorous "a posteriori" error bound,
(ii) employing the successive constraints method to efficiently calculate a lower bound for the solution-dependent inf-sup stability constant, while preserving the efficient offline-online computational procedure.

Time: 02:00 pm

Location: Room 149, Hauptgebäude, RWTH Aachen, Templergraben 55, 52056 Aachen