Study of a non-overlapping domain decomposition method: Steady Navier–Stokes equations

Abstract

In [C. R. Acad. Sci. Paris Ser. I 334 (2002) 221] and [Appl. Numer. Math. 48 (2004) 169] we presented a non-overlapping decomposition method via a penalization on the interface and study its application to the Poisson and Stokes problems. In this work we extend this study to the case of the steady Navier–Stokes equations and find that the technique is well suited for moderate Reynolds number flows. Under the usual regularity assumptions on the true solution, we obtain error estimates in the natural norms that are optimal in terms of the space discretization in the sense that we obtain an O ( h k ) error estimate when we use a space approximation of order k. We conclude with some numerical tests.