The L2 Norm Error Estimates for the Div Least-Squares Method

Abstract. This paper studies L2 norm error estimates for the div least-squares method for which the associated homogeneous least-squares functional is equivalent to the H(div) × H1 norm for the respective dual and primal variables. Least-squares of this type for the second-order elliptic equations, elasticity, and the Stokes equations are an active area of research, and error estimates in the H(div) × H1 norm were previously established. In this paper, we establish optimal L2 norm error estimates for the primal variable under the minimum regularity requirement through a refined duality argument.