NUMERICAL ANALYSIS ON THE SIERPINSKI GASKET, WITH APPLICATIONS TO SCHRÖDINGER EQUATIONS, WAVE EQUATION, AND GIBBS' PHENOMENON

Abstract

We show how to improve the finite element method on the Sierpinski gasket (SG) to allow arbitrary partitions of the space. We use this method to study numerically solutions of the Schrödinger equation with well-type potentials, and the wave equation. We also show that Fourier series-type expansions on SG of functions with jump discontinuities appear to exhibit a self-similar Gibbs' phenomenon.