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The steps above can be abbreviated as a fixed-point Gauss-Seidel problem 

 with respect to the interface displacement, which is to be solved until convergence of the corresponding residuals 

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 . Typical convergence norms are  

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 which makes the norm independent on the interface mesh size or relative convergence

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. Note that the cost of evaluation of  

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 is high and it may contain noise/errors (for example due to not fully converged solvers).

Various methods can be used to ensure and accelerated convergence of the root-finding problem. A (dynamic) under-relaxation is 

. For example Aitken under-relaxation is given by

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.