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A Least-Squares Finite Element Reduced Basis Method (2003.04555v2)

Published 10 Mar 2020 in math.NA and cs.NA

Abstract: We present a reduced basis (RB) method for parametrized linear elliptic partial differential equations (PDEs) in a least-squares finite element framework. A rigorous and reliable error estimate is developed, and is shown to bound the error with respect to the exact solution of the PDE, in contrast to estimates that measure error with respect to a finite-dimensional (high-fidelity) approximation. It is shown that the first-order formulation of the least-squares finite element is a key ingredient. The method is demonstrated using numerical examples.

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