Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-10-172001enWe present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced-basis approximations—Galerkin projection onto a space WN spanned by solutions of the gov- erning partial differential equation at N selected points in parameter space; (ii) a poste- riori error estimation—relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/ on-line computational procedures methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time controhttp://creativecommons.org/licenses/by/4.0/Journal of Fluids Engineering112470-80 Rovas Dimitrios Ροβας Δημητριος Veroy, Karen Patera, Adolf, 1836-1912 Turinici, Gabriel L. Machiels C. Prud’homme American Society of Mechanical Engineers Greek mathematics mathematics greek greek mathematics