L 2 error estimates for a nonstandard finite element method on polyhedral meshes

Abstract

Recently, Hofreither, Langer and Pechstein have analyzed a nonstandard finite element method based on element-local boundary integral operators. The method is able to treat general polyhedral meshes and employs locally PDE-harmonic trial functions. In the previous work, the primal formulation of the method has been analyzed as an inexact Galerkin scheme, obtaining H1 error estimates. In this work, we pass to an equivalent mixed formulation. This allows us to derive error estimates in the L2-norm, which were so far not available. Many technical tools from our previous analysis remain applicable in this setting.