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

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