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

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.

References in corpus (2)

• On commuting $p$-version projection-based interpolation on tetrahedra
• Wavenumber-explicit $hp$-FEM analysis for Maxwell's equations with transparent boundary conditions

Cited by in corpus (1)

• Aubin--Nitsche-type estimates for space-time FOSLS for parabolic PDEs