  This work presents a strongly coupled partitioned method for fluid-structure
interaction (FSI) problems based on a monolithic formulation of the system
which employs a Lagrange multiplier. We prove that both the semi-discrete and
fully discrete formulations are well-posed. To derive a partitioned scheme, a
Schur complement equation, which implicitly expresses the Lagrange multiplier
and the fluid pressure in terms of the fluid velocity and structural
displacement, is constructed based on the monolithic FSI system. Solving the
Schur complement system at each time step allows for the decoupling of the
fluid and structure subproblems, making the method non-iterative between
subdomains. We investigate bounds for the condition number of the Schur
complement matrix and present initial numerical results to demonstrate the
performance of our approach, which attains the expected convergence rates.
