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hide some of the complexity by automatically assessing the convergence: `IterativeLoop` uses an empirical algorithm for calculating the error whereas `IterativeLoopN` allows to specify
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in detail the error calculation and the allowed tolerances.
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In all cases, several functions can be used to generate the linear system (`Generate`) and the Jacobian matrix (`GenerateJac`) and the associated right-hand sides. The function (`GetResidual`) can also be used to explicitly evaluate the residual (see below).
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## Nonlinear solvers
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For linear problems, the finite element method leads to the solution of linear
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\quad k = 0, 1, 2, ...
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```
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### Convergence assessment
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<!--
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For the exact solution, the residual defined by $\vec{r}(\vec{x})=\mat{A}(\vec{x}) \; \vec{x}-\vec{b}$ is zero. If after $p$ iterations, a satisfactory convergence is obtained, the iterative process is stopped. The convergence criterion could be based on some norm of the residual $\vec{r}(\vec{x}_p)$ or on the $p^\text{th}$ increment $\vec{\delta x}_p=\vec{x}_p-\vec{x}_{p-1}$. For example, it could be :
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