Mesh Optimization and Multilevel Finite Element Approximations

Mesh reduction techniques are used for accelerating the visualization process for large datasets. Typical examples are scalar or vector valued functions deened on complex 2 or 3 dimensional meshes. Grosso et al. presented a method for mesh optimization based on nite elements approximations with the L2 norm and adaptive local mesh reenement. Starting with a very coarse triangulation of the functional domain a hierarchy of highly non-uniform tetrahedral (or triangular in 2D) meshes is generated adaptively by local reenement. This process is driven by controlling the local error of the piecewise linear nite element approximation of the function on each mesh element. In this paper we extend the algorithm to the Sobolev space H 1 , where the error norm allows for gradient information to be included. This improves the convergence of the algorithm in regions, where the function has high frequency oscillations. In order to analyze the properties of the optimized meshes we consider iso-surfaces of volume data.