Rapid Reliable Solution
of the Parametrized Partial Differential Equations
of Continuum Mechanics and Transport

Webserver Version

The "Graetz" Problem
Forward Problem

Authors: G Rozza & AT Patera
in collaboration with DBP Huynh & NC Nguyen

Evaluation and Visualization Module

The user should first input the parameter μ = [μ1, μ2] such that μ in [1, 10] × [0.1, 100]. The user should also input a numerical parameter that relates to the desired accuracy of the RB output prediction Npr in [1, 36], Ndu in [1, 32]: the error in our prediction decreases as N increases.

The code then displays, for the desired parameter value μ = [μ1, μ2], (i) the contour of the field, and (ii) the value of the output/quantity of interest. In each case, we also provide a certificate of fidelity that rigorously bounds the error in our RB prediction relative to the highly accurate (and hence very expensive) "truth'' Finite Element solution.

μ1 in [1, 10]:

μ2 in [0.1, 100]:

Npr in [1, 36]:

Ndu in [1, 32]:

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