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The numerical approximation of incompressible fluid-structure interactionproblems with Lagrange multiplier is generally based on strongly coupledschemes. This delivers unconditional stability but at the expense of solving acomputationally demanding coupled system at each time-step. For the case of thecoupling with immersed thin-walled solids, we introduce a class ofsemi-implicit coupling schemes which avoids strongly coupling withoutcompromising stability and accuracy. A priori energy and error estimates arederived. The theoretical results are illustrated through numerical experimentsin an academic benchmark.

Splitting schemes for a Lagrange multiplier formulation of FSI with immersed thin-walled structure: stability and convergence analysis