Optimal convergence rates in $L^2$ for a first order system least squares finite element method. Part I: homogeneous boundary conditions (2012.12919v1)

Abstract: We analyze a divergence based first order system least squares method applied to a second order elliptic model problem with homogeneous boundary conditions. We prove optimal convergence in the $L^2(\Omega)$ norm for the scalar variable. Numerical results confirm our findings.