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When is good, good enough? This question lingers in approximation theory andnumerical methods as a competition between accuracy and practicality. NumericalAnalysis is traditionally where the rubber meets the road: students begin touse numerical algorithms to compute approximate solutions to non-trivialproblems. However, it is difficult for students to understand that moreaccuracy is not always the goal, but rather enough accuracy for practical useand meaningful interpretation. This compromise between accuracy andcomputational time/resources can be explored through the use of convergenceplots. We offer a variety of classroom activities that allow students todiscover the usefulness of convergence plots, including a contemporary exampleinvolving jellyfish locomotion using fluid-structure interaction modeling.These examples will additionally illustrate subtleties of convergence analysis:the same numerical scheme can exhibit different convergence rates, and thedefinition of `error' may change the convergence properties. To solve thefluid-structure interaction system, the open source software IB2d is used. Allnumerical codes, scripts, and movies are provided for streamlined integrationinto a classroom setting.

Fluid-Structure Interaction for the Classroom: Speed, Accuracy, Convergence, and Jellyfish!