First-order system least squares for second-order partial differential equations: Part I

This paper develops ellipticity estimates and discretization error bounds for elliptic equations (with lower-order terms) that are reformulated as a least-squares problem for an equivalent first-order system. The main result is the proof of ellipticity, which is used in a companion paper to establish optimal convergence of multiplicative and additive solvers of the discrete systems.

First-order system least squares for second-order partial differential equations: Part I Academic Article