Tangential Errors of Tensor Surface Finite Elements

TL;DR

This paper investigates the discretization of tangential tensor field equations on surfaces using finite element methods, demonstrating optimal convergence properties especially with an isogeometric penalization approach based on geometric information.

Contribution

It introduces a surface-finite element method with penalization for tangential tensor fields and proves optimal convergence behavior intrinsically for tangential quantities.

Findings

Optimal order convergence for tangential quantities

Effective isogeometric penalization based on geometric data

Intrinsic measurement of discretization quality

Abstract

We discretize a tangential tensor field equation using a surface-finite element approach with a penalization term to ensure almost tangentiality. It is natural to measure the quality of such a discretization intrinsically, i.e., to examine the tangential convergence behavior in contrast to the normal behavior. We show optimal order convergence with respect to the tangential quantities in particular for an isogeometric penalization term that is based only on the geometric information of the discrete surface.