Anisotropic mesh adaptation through hierarchical error estimators

A posteriori error estimation and its use in mesh adaptation procedures has become one of the principal axes of development in the numerical analysis of partial differential equations. This paper would like to give a new insight on an anisotropic mesh adaptation technique which is based on a hierarchical error estimate. A simplified version will use information from a higher order reinterpolations of the solution. Even if they lack a complete mathematical justification, experimental evidence clearly shows that these methods work very well and that they provide a way to drive anisotropic mesh adaptation. Such anisotropic capabilities have led to spectacular results in the simulation of compressible flows with shocks([13], [11]). We present here a short description of the methodology and its underlying principles.

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