Optimal A Priori Discretization Error Bounds for Geodesic Finite Elements

@article{Grohs2015OptimalAP,
  title={Optimal A Priori Discretization Error Bounds for Geodesic Finite Elements},
  author={Philipp Grohs and Hanne Hardering and Oliver Sander},
  journal={Foundations of Computational Mathematics},
  year={2015},
  volume={15},
  pages={1357-1411}
}
We prove optimal bounds for the discretization error of geodesic finite elements for variational partial differential equations for functions that map into a nonlinear space. For this we first generalize the well-known Céa lemma to nonlinear function spaces. In a second step we prove optimal interpolation error estimates for pointwise interpolation by geodesic finite elements of arbitrary order. These two results are both of independent interest. Together they yield optimal a priori error… CONTINUE READING