An Alternative Proof of a Strip Estimate for First-Order System Least-Squares for Interface Problems

The purpose of this paper is an alternative proof of a strip estimate, used in Least-Squares methods for interface problems, as in [4] for a two-phase flow problem with incompressible flow in the subdomains. The Stokes flow problems in the subdomains are treated as first-order systems and a combination of H(div)-conforming Raviart-Thomas and standard H-1-conforming elements were used for the discretization. The interface condition is built directly in the H(div)-conforming space. Using the strip estimate, the homogeneous Least-Squares functional is shown to be equivalent to an appropriate norm allowing the use of standard finite element approximation estimates.