Highly Influenced

4 Excerpts

- Published 1997 in Math. Comput.

Solutions of the so-called prescribed curvature problem minA⊆Ω PΩ(A)− ∫ A g(x), g being the curvature field, are approximated via a singularly perturbed elliptic PDE of bistable type. For nondegenerate relative minimizers A ⊂⊂ Ω we prove an O( 2| log |2) error estimate (where stands for the perturbation parameter), and show that this estimate is quasi-optimal. The proof is based on the construction of accurate barriers suggested by formal asymptotics. This analysis is next extended to a finite element discretization of the PDE to prove the same error estimate for discrete minima.

@article{Paolini1997AQE,
title={A quasi-optimal error estimate for a discrete singularly perturbed approximation to the prescribed curvature problem},
author={Maurizio Paolini},
journal={Math. Comput.},
year={1997},
volume={66},
pages={45-67}
}