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<span class="gras"><b>Content</b></span><br /> | <span class="gras"><b>Content</b></span><br /> | ||

- | I - Boundary problems and variational forms. Spaces of Sobolev.\\ | + | I - Boundary problems and variational forms. Spaces of Sobolev.<br> |

- | II - Stationary models / Elliptic equations\\ | + | II - Stationary models / Elliptic equations<br> |

- | Variational framework. Symmetric case and link minimization. Formulas of Green.\\ | + | Variational framework. Symmetric case and link minimization. Formulas of Green.<br> |

- | III - Introduction to modeling from a few examples: Thermal (1D / 2D, Stationary / unsteady), transport, elasticity (Lamé) and fluids (Stokes), fluid-structure coupling (flow around an elastic obstacle). Discussion of the mathematical difficulties specific to each type of phenomenon.\\ | + | III - Introduction to modeling from a few examples: Thermal (1D / 2D, Stationary / unsteady), transport, elasticity (Lamé) and fluids (Stokes), fluid-structure coupling (flow around an elastic obstacle). Discussion of the mathematical difficulties specific to each type of phenomenon.<br> |

- | IV - Finite element method: basic functions, algorithms, implementation, a priori error analysis. Term of transport and stabilization. Nonlinear case and linearization.\\ | + | IV - Finite element method: basic functions, algorithms, implementation, a priori error analysis. Term of transport and stabilization. Nonlinear case and linearization.<br> |

- | IV - Unsteady models / Parabolic equations.\\ | + | IV - Unsteady models / Parabolic equations.<br> |

- | Temporal schemes and splitting methods. Diagrams DF - EF.\\ | + | Temporal schemes and splitting methods. Diagrams DF - EF.<br> |

IV - Possible extensions: ALE method for fluid-structure coupling, model reduction, discontinuous Galerkin, a posteriori analysis and mesh refinement. Some of these extensions can be addressed in the context of the TP.<br /><br /><br /> | IV - Possible extensions: ALE method for fluid-structure coupling, model reduction, discontinuous Galerkin, a posteriori analysis and mesh refinement. Some of these extensions can be addressed in the context of the TP.<br /><br /><br /> | ||