An hp certified reduced basis method for parametrized parabolic partial differential equations

Jens L. Eftang, David J. Knezevic and Anthony T. Patera

Mathematical and Computer Modelling of Dynamical Systems, 2010, vol. 17, issue 4, 395-422

Abstract: In this article, we introduce an hp certified reduced basis (RB) method for parabolic partial differential equations. We invoke a Proper Orthogonal Decomposition (POD) (in time)/Greedy (in parameter) sampling procedure first in the initial partition of the parameter domain ( h -refinement) and subsequently in the construction of RB approximation spaces restricted to each parameter subdomain ( p -refinement). We show that proper balance between additional POD modes and additional parameter values in the initial subdivision process guarantees convergence of the approach. We present numerical results for two model problems: linear convection--diffusion and quadratically non-linear Boussinesq natural convection. The new procedure is significantly faster (more costly) in the RB Online (Offline) stage.

Date: 2010
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DOI: 10.1080/13873954.2011.547670

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