An "hp" Certified Reduced Basis Method for Parametrized Elliptic Partial Differential Equations

We present a new "hp" parameter multi-domain certified reduced basis method for rapid and reliable online evaluation of functional outputs associated with parametrized elliptic partial differential equations. We propose, and provide theoretical justification for, a new procedure for adaptive partition ("h"-refinement) of the parameter domain into smaller parameter subdomains: we pursue a hierarchical splitting of the parameter (sub)domains based on proximity to judiciously chosen parameter anchor points within each subdomain. Subsequently, we construct individual standard RB approximation spaces ("p"-refinement) over each subdomain. Greedy parameter sampling procedures and a posteriori error estimation play important roles in both the "h"-type and "p"-type stages of the new algorithm. We present illustrative numerical results for a convection-diffusion problem: the new "hp"-approach is considerably faster (respectively, more c...

• Type: Journal
• Year: 2010
• Where: SIAMSC
• Authors: Jens L. Eftang, Anthony T. Patera, Einar M. Rønquist
• Keywords: Parameter, Parameter Domain, Posteriori Error Estimation, SIAMSC 2010