A penalty-free Shifted Boundary Method of arbitrary order

TL;DR

This paper presents a penalty-free, high-order Shifted Boundary Method that is proven to be exactly consistent, stable, and convergent, with demonstrated numerical performance.

Contribution

It introduces a novel penalty-free formulation of the SBM, proves its exact consistency and stability for arbitrary order finite elements, and validates it through numerical experiments.

Findings

Proves the exact consistency of the SBM.

Establishes stability and convergence for arbitrary order spaces.

Demonstrates numerical effectiveness through experiments.

Abstract

We introduce and analyze a penalty-free formulation of the Shifted Boundary Method (SBM), inspired by the asymmetric version of the Nitsche method. We prove its stability and convergence for arbitrary order finite element interpolation spaces and we test its performance with a number of numerical experiments. Moreover, while the SBM was previously believed to be only asymptotically consistent (in the sense of Galerkin orthogonality), we prove here that it is indeed exactly consistent.