Article,

On Optimal L2 and Surface Flux Convergence in FEM

, , and .
(2014)

Abstract

We show that optimal L 2 -convergence in the finite element method on quasi-uniform meshes can be achieved if the underlying boundary value problem admits a shift theorem by more than 1 / 2 . For this, the lack of full elliptic regularity in the dual problem has to be compensated by additional regularity of the exact solution. Furthermore, we analyze for a Dirichlet problem the approximation of the normal derivative on the boundary without convexity assumption on the domain. We show that (up to logarithmic factors) the optimal rate is obtained.

Tags

Users

  • @gdmcbain

Comments and Reviews