## Ajustement spline le long d’un ensemble de courbes. (Spline adjustment along a set of curves).(French)Zbl 0725.65017

Authors’ summary: For a surface defined by an explicit equation $$x_ 3=f(x_ 1,x_ 2)$$, the problem of constructing a smooth approximant from a finite set of curves given on the surface is studied. As an approximant of f, a “discrete smoothing spline” belonging to a suitable finite element space is proposed. Convergence of the method and numerical results are given.

### MSC:

 65D17 Computer-aided design (modeling of curves and surfaces) 65D07 Numerical computation using splines
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### References:

 [1] D. APPRATO, R. ARCANGÉLI, R. MANZANILLA, Sur la construction de surfaces de classe Ck à partir d’un grand nombre de données de Lagrange M2AN,vol. 21, n^\circ 4, 529-555 (1987). Zbl0632.65011 MR921826 · Zbl 0632.65011 [2] R. ARCANGÉLI, Cours de DEA, Pau, à paraître. [3] P.G. CIARLET, The Finite Element Method for Elliptic Problems, North Holland, Amsterdam (1978). Zbl0383.65058 MR520174 · Zbl 0383.65058 [4] P. G. CIARLET, P.-A. RAVIART, General Lagrange and Hermite Interpolationin Rn with Applications to Finite Element Methods, Arch. Rat. Mech. Anal., 46, 177-199 (1972). Zbl0243.41004 MR336957 · Zbl 0243.41004 [5] P. CLÉMENT, Approximation by Finite Element Functions Using Local Regularization, RAIRO, 9e année, R-2, 77-84 (1975). Zbl0368.65008 MR400739 · Zbl 0368.65008 [6] J. DUCHON, Splines Minimizing Rotation-Invariant Semi-Norms in Sobolev Spaces, Lecture Notes in Math., 571, 85-100, Springer (1977). Zbl0342.41012 MR493110 · Zbl 0342.41012 [7] P. GRISVARD, Elliptic Problems in Nonsmooth Domains, Pitman, Boston (1985). Zbl0695.35060 MR775683 · Zbl 0695.35060 [8] J. NEČAS, Les méthodes directes en théorie des équations elliptiques, Masson, Paris (1967). MR227584 · Zbl 1225.35003 [9] J. PEETRE, Espaces d’interpolation et théorème de Soboleff, Ann. Inst. Fourier,Grenoble, 16, 279-317 (1966). Zbl0151.17903 MR221282 · Zbl 0151.17903 [10] G. STRANG, Approximation in the Finite Element Method, Numer. Math., 19, 81-98 (1972). Zbl0221.65174 MR305547 · Zbl 0221.65174 [11] A. ŽENISEK, A General Theorem on Triangular Finite C(m)-Elements RAIRO, R-2, 119-127 (1974). Zbl0321.41003 MR388731 · Zbl 0321.41003
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