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Optimal anisotropic meshes for minimizing interpolation errors in  -norm |
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| Authors: | Long Chen Pengtao Sun Jinchao Xu |
| Institution: | Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802 Pengtao Sun ; Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802 ; The School of Mathematical Science, Peking University, Beijing, People's Republic of China; and Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802 |
| Abstract: | In this paper, we present a new optimal interpolation error estimate in  norm (  ) 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 viewpoint of minimizing interpolation error in the  norm. Some numerical examples are also given to support the theoretical estimates. |
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