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__Inexact Fixed Point Schemes and Applications in Scientific Computing__

P. Birken

**Abstract**

We consider fixed point schemes, where the function evaluation corresponds to inexact solves of linear or nonlinear equation systems. This allows to decide how accurate these systems should be solved to obtain a target error in the fixed point iteration, as well as to decide on a good termination criterion.
The first applicaton is the Picard iteration which is widely used for the incompressible Navier-Stokes equations. Here we can show that this iteration converges regardless of how accurate we solve the subsystems, provided a relative termination criterion is employed.
As a second example, we consider thermal fluid structure interaction problems where heat is exchanged via a coupling interface. This appears in many applications, for example in the cooling
process in steel forging. A so called partitioned coupling approach naturally leads to a fixed point iteration, which is then analyzed using the derived methodology.