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Titlebook: Certified Reduced Basis Methods for Parametrized Partial Differential Equations; Jan S Hesthaven,Gianluigi Rozza,Benjamin Stamm Book 2016

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Lernen aus dem paradigmatischen Wandel?, apply the reduced basis methodology to more complex problems of their own interest. The extensions are related to (i) time-dependent problems, (ii) geometrical parametrization of the computational domain and (iii) non-compliant outputs and primal-dual approximations, and (iv) non-coercive problems.
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,Aufklärung oder Motivation des Patienten,The development of effective and reliable a posteriori error estimators for the field variable or an output of interest is crucial to ensure the reliability and efficiency of the reduced basis approximations. Reduced basis approximations are problem dependent since discretizations are problem specific.
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Erkennen der Krankheitsursache (Diagnose),o seek alternatives to simply solving the full problem many times. This is exactly where reduced models have its place and we are now ready to dive deeper into a discussion of central elements of the certified reduced basis method.
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