Geodesic
On local refinement of smooth finite elements and splines
Matematičeskoe modelirovanie, Tome 14 (2002) no. 5, pp. 109-115.

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We present an algorithm of local refinement of finite-element and spline approximations based on a uniform refinement of the mesh. Since a local mesh refinement is not needed, the method is in particular applicable to low order smooth polynomial splines on uniform type triangulations, tensor product and box splines as well as some smooth composite finite elements. The algorithm can be used in the context of adaptive approximation methods. 
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     author = {O. V. Davydov},
     title = {On local refinement of smooth finite elements and splines},
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O. V. Davydov. On local refinement of smooth finite elements and splines. Matematičeskoe modelirovanie, Tome 14 (2002) no. 5, pp. 109-115. http://geodesic.mathdoc.fr/item/MM_2002_14_5_a10/

[1] O. Davydov, “Stable local bases for multivariate spline spaces”, J. Approx. Theory (to appear)

[2] O. Davydov, “On the computation of stable local bases for bivariate polynomial splines”, Trends in Approximation Theory, eds. K. Kopotun, T. Lyche, M. Neamtu, Vanderbilt University Press (to appear) | MR

[3] O. Davydov, Locally stable spline bases on nested triangulations, manuscript, 2001 | MR

[4] \уто O. Davydov, L. L. Schumaker, “Stable local nodal bases for $C^1$ bivariate polynomial splines”, Curve and Surface Fitting: Saint-Malo 1999, eds. A. Cohen, C. Rabut, L. L. Schumaker, Vanderbilt University Press, 2000, 171–180

[5] O. Davydov, L. L. Schumaker, “On stable local bases for bivariate polynomial spline spaces”, Constr. Approx. (to appear) | MR