Geodesic
The choice of the weight coefficients for the least-squares gradient approximation
Matematičeskoe modelirovanie, Tome 16 (2004) no. 5, pp. 83-93

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We consider the problem of the least-squares gradient approximation on two-dimensional unstructured grids with “bad” cells. We discuss how the accuracy of the least-squares approximation depends on the cell geometry. We analyze a simple geometry and demonstrate that introducing weight coefficients into the problem may help to essentially improve the accuracy of the least-squares approximation. Based on the results of our analysis, a heuristic choice of the weights in a general least-squares procedure is suggested. Our approach is illustrated by numerical tests. 
@article{MM_2004_16_5_a6,
     author = {N. B. Petrovskaya},
     title = {The choice of the weight coefficients for the least-squares gradient approximation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {83--93},
     publisher = {mathdoc},
     volume = {16},
     number = {5},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2004_16_5_a6/}
}
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N. B. Petrovskaya. The choice of the weight coefficients for the least-squares gradient approximation. Matematičeskoe modelirovanie, Tome 16 (2004) no. 5, pp. 83-93. http://geodesic.mathdoc.fr/item/MM_2004_16_5_a6/