  The numerical approximation of incompressible fluid-structure interaction
problems with Lagrange multiplier is generally based on strongly coupled
schemes. This delivers unconditional stability but at the expense of solving a
computationally demanding coupled system at each time-step. For the case of the
coupling with immersed thin-walled solids, we introduce a class of
semi-implicit coupling schemes which avoids strongly coupling without
compromising stability and accuracy. A priori energy and error estimates are
derived. The theoretical results are illustrated through numerical experiments
in an academic benchmark.
