Communications in Analysis and Geometry
Volume 14 (2006)
Error Estimates for Discrete Harmonic 1-forms over Riemann Surfaces
Pages: 1027 – 1035
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 Poincaré inequality over a triangle of arbitrary shape.