An hp Certified Reduced Basis Method for Parametrized Parabolic Partial Differential Equations
We extend previous work on a parameter multi-element hp certified reduced basis method for elliptic equations to the case of parabolic equations. A POD (in time)/Greedy (in parameter) sampling procedure is invoked both in the partitioning of the parameter domain (h-refinement) and in the construction of individual reduced basis approximation spaces for each parameter subdomain (p-refinement). The critical new issue is proper balance between additional POD modes and additional parameter values in the initial subdivision process. We present numerical results to compare the computational cost of the new approach to the standard (p-type) reduced basis method.
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