During this thesis we have investigate two important fields of the anisotropic meshes adaptation problems which are: - Metrics and errors estimators, - the locals modifications of hexahedral and quadrilateral meshes. We propose new algorithms, methods and numerical schemes within this two parts. We add new methods of building errors estimators and metrics in the software Freefem++. We have work about some hessian matrix recovery techniques, as second order error estimator of the Lagrange polynomial interpolation which are: - The last square recovery method, - the method based on the Green formula, - the local approximation of the function by a second degree polynomial. We propose a new recovery technique which uses a local interpolation inside each element of the mesh and a finite difference scheme. we show some properties like con- sistence and convergence of all these methods and numerical results in dimension two of the space. We study the third order derivatives recovery using the least square tech- nique. We also propose a new calculation of the Lagrange interpolation error estimator. This result uses a Taylor development of the third order without any direct calculus of third other derivatives. We also propose an algorithm for building metrics using any given error estimation that can be represented by a close curve. We finally propose a new set of local hex meshes transformations and a study about the existing local quad and hex meshes modifications by showing some new properties.
展开▼
