Abstract
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 \(H ({\text {div}})\)-conforming Raviart-Thomas and standard \(H^1\)-conforming elements were used for the discretization. The interface condition is built directly in the \(H ({\text {div}})\)-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.
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Bertrand, F. (2018). An Alternative Proof of a Strip Estimate for First-Order System Least-Squares for Interface Problems. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science(), vol 10665. Springer, Cham. https://doi.org/10.1007/978-3-319-73441-5_9
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