An improved a priori error analysis of Nitsche's method for Robin boundary conditions

TL;DR

This paper presents an improved a priori error analysis for Nitsche's method applied to Robin boundary conditions, reducing regularity requirements using Gudi's technique.

Contribution

It introduces a novel error analysis approach for Nitsche's method that requires less regularity of the solution compared to previous work.

Findings

Enhanced error bounds for Nitsche's method

Reduced regularity assumptions for solutions

Application to Robin boundary conditions

Abstract

In a previous paper [6] we have extended Nitsche's method [8] for the Poisson equation with general Robin boundary conditions. The analysis required that the solution is in H^s, with s > 3/2. Here we give an improved error analysis using a technique proposed by Gudi [5].