Nitsche's method for a Robin boundary value problem in a smooth domain

Abstract

AbstractWe prove several optimal‐order error estimates for a finite‐element method applied to an inhomogeneous Robin boundary value problem (BVP) for the Poisson equation defined in a smooth bounded domain in , . The boundary condition is weakly imposed using Nitsche's method. The Robin BVP is interpreted as the classical penalty method with the penalty parameter . The optimal choice of the mesh size relative to is a non‐trivial issue. This paper carefully examines the dependence of on error estimates. Our error estimates require no unessential regularity assumptions on the solution. Numerical examples are also reported to confirm our results.