in a past life i learned a little about PDE and the theory justifying why finite element methods work to approximate solutions.

i never explicitly ran into anything about discrete differential geometry, but that doesn't mean it wasn't there all along, lurking beneath (or perhaps above?) my level of understanding.

some reading: Evans -- Partial Differential Equations, Wendland -- Scattered Data Approximation, Wahba -- Spline models for observational data .