Geodesic
Hessian-free metric-based mesh adaptation via geometry of interpolation error
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 1, pp. 131-145

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The article presents analysis of a new methodology for generating meshes minimizing $L^p$-norms of the interpolation error or its gradient, $p>0$. The key element of the methodology is the construction of a metric from node-based and edge-based values of a given function. For a mesh with $N_h$ triangles, we demonstrate numerically that $L^\infty$-norm of the interpolation error is proportional to $N_h^{-1}$ and $L^\infty$-norm of the gradient of the interpolation error is proportional to $N_h^{-1/2}$. The methodology can be applied to adaptive solution of PDEs provided that edge-based a posteriori error estimates are available. 
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     author = {A. Agouzal and K. N. Lipnikov and Yu. V. Vassilevski},
     title = {Hessian-free metric-based mesh adaptation via geometry of interpolation error},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     year = {2010},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_1_a10/}
}
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A. Agouzal; K. N. Lipnikov; Yu. V. Vassilevski. Hessian-free metric-based mesh adaptation via geometry of interpolation error. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 1, pp. 131-145. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_1_a10/