MFC
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Add `examples/` into CI
Make each example case sufficiently small such that it can run on one processor for at least a few time steps. Then, add a few time steps of each example case to CI and set I/O to write at the end. Then check output for NaNs/Inftys.
We grow the size of the test suite this way, though it isn't as thorough a test as there will be no goldenfiles (though I suppose we could add them).