  When is good, good enough? This question lingers in approximation theory and
numerical methods as a competition between accuracy and practicality. Numerical
Analysis is traditionally where the rubber meets the road: students begin to
use numerical algorithms to compute approximate solutions to non-trivial
problems. However, it is difficult for students to understand that more
accuracy is not always the goal, but rather enough accuracy for practical use
and meaningful interpretation. This compromise between accuracy and
computational time/resources can be explored through the use of convergence
plots. We offer a variety of classroom activities that allow students to
discover the usefulness of convergence plots, including a contemporary example
involving 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 the
definition of `error' may change the convergence properties. To solve the
fluid-structure interaction system, the open source software IB2d is used. All
numerical codes, scripts, and movies are provided for streamlined integration
into a classroom setting.
