A4

Long Chen, Pengtao Sun and Jinchao Xu. Optimal anisotropic simplicial meshes for minimizing interpolation errors in ${L}^p$-norm. Mathematics of Computation (In Press), :, 2006.

Chen.L;Sun.P;Xu.J2006.pdf

ABSTRACT: In this paper, we present a new optimal interpolation error estimate in $L^p$ norm ($1\leq p\leq \infty$) for finite element simplicial meshes in any spatial dimension. A sufficient condition for a mesh to be nearly optimal is that it is quasi-uniform under a new metric defined by a modified Hessian matrix of the function to be interpolated. We also give new functionals for the global moving mesh method and obtain optimal monitor functions from the view points of minimizing interpolation error in the $L^p$ norm. Some numerical examples are also given to support the theoretical estimates.