Error estimates for discrete harmonic 1-forms over Riemann surfaces

摘要

We derive L-2 error estimates of computing harmonic or holomorphic 1-forms over a Riemann surface via finite element methods. Locally constant finite elements and first order approximations of the Riemann surface by triangulated meshes are considered. We use in the proof a Bochner type formula and a refined Poincare inequality over a triangle of arbitrary shape.