Optimal convergence rates in L² for a first order system least squares finite element method - part II: Inhomogeneous Robin boundary conditions

Abstract

We consider divergence-based high order discretizations of an L2-based first order system least squares formulation of a second order elliptic equation with Robin boundary conditions. For smooth geometries, we show optimal convergence rates in the L2(Ω)-norm for the scalar variable. Convergence rates for the L2(Ω)-norm error of the gradient of the scalar variable as well as the vectorial variable are also derived. Numerical examples illustrate the analysis.