  We present a monolithic approach to large-deformation fluid-structure
interaction (FSI) problems that allows for choosing fully implicit, single-step
and single-stage time integration schemes in the structure and fluid field
independently, and hence is tailored to the needs of the individual field. The
independent choice of time integration schemes is achieved by temporal
consistent interpolation of the interface traction. To reduce computational
costs, we introduce the possibility of field specific predictors in both
structure and fluid field. These predictors act on the single fields only.
Possible violations of the interface coupling conditions during the predictor
step are dealt with within the monolithic solution procedure. We present full
detail of such a generalized monolithic solution procedure, which is fully
consistent in its non-conforming temporal and spatial discretization. The
incorporated mortar approach allows for non-matching spatial discretizations of
the fluid and solid domain at the FSI interface and is fully integrated in the
resulting monolithic system of equations. The method is applied to a variety of
numerical examples. Thereby, temporal convergence rates, the special role of
essential boundary conditions at the fluid-structure interface, and the
positive effect of predictors are demonstrated and discussed. Emphasis is put
on the comparison of different time integration schemes in fluid and structure
field, for what the achieved freedom of choice of time integrators is fully
exploited.
