A penalty free non-symmetric Nitsche type method for the weak imposition of boundary conditions

TL;DR

This paper introduces a penalty-free non-symmetric Nitsche method for weak boundary condition imposition, demonstrating stability and optimal error estimates for diffusion and convection-diffusion problems without penalty parameters.

Contribution

It presents a novel penalty-free non-symmetric Nitsche method that ensures stability and optimal error bounds for boundary condition enforcement.

Findings

Stable without penalty term

Optimal H^1-error estimates

Suboptimal L^2-error estimates by half an order

Abstract

In this note we show that the non-symmetric version of the classical Nitsche's method for the weak imposition of boundary conditions is stable without penalty term. We prove optimal $H^1$-error estimates and $L^2$-estimates that are suboptimal with half an order in $h$. Both the pure diffusion and the convection--diffusion problems are discussed.