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A trivariate box macroelement. (English) Zbl 1077.41009
The subject of this article is the construction of polynomial spline macroelements in three dimensions. Some of the most often used macroelements, e.g. in the numerical solution of partial differential equations, are continuously differentiable, so this is what the authors are looking for in the paper. For this $$C^1$$ macroelement, polynomials of total degree six are used, and the macroelement is constructed on the basis of a rectangular box which is subdivided into 24 tetrahedra. For this, the usual Bernstein-Bézier representation is used. Hermite interpolation, the important question of the dimension of the spline space, and the accuracy of approximation using these elements are also discussed.

##### MSC:
 41A15 Spline approximation
##### Keywords:
trivariate splines; macroelements; Hermite interpolation
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