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Approximation by finite element functions using local regularization. (English) Zbl 0368.65008

MSC:
65D10 Numerical smoothing, curve fitting
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
41A30 Approximation by other special function classes
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References:
[1] Ph. CLEMENT, Un problème d’approximation par éléments finis, Annexe à la thèse de Doctorat, Ecole Polytechnique Fédérale de Lausane, 1973.
[2] J. J GOEL, Construction of Basic Functions for Numerical Utilisation of Ritz-s Method, Numer. Math., (1968), 12, 435-447. Zbl0271.65061 MR256580 · Zbl 0271.65061
[3] M. ZLAMAL, On the Finite Element Method, Numer. Math., (1968), 12, 394-409. Zbl0176.16001 MR243753 · Zbl 0176.16001
[4] J. H. BRAMBLE and M. ZLAMAL, Triangular Elements in the Finite Element Method, Math. of Comp. vol. 24, number 12, (1970), 809-820. Zbl0226.65073 MR282540 · Zbl 0226.65073
[5] G. STRANG, Approximation in the finite element method, Numer Math., (1972), 19, 81-98. Zbl0221.65174 MR305547 · Zbl 0221.65174
[6] G DUPUIS et J. J. GOEL, Eléments finis raffinés en élasticité bidimensionnelle, ZAMP, vol. 20, (1969), 858-881. Zbl0201.26604 · Zbl 0201.26604
[7] J. DESCLOUX, Méthodes des éléments finis, Dept. de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, 1973.
[8] J. DESCLOUX, Two Basic Properties of Finite Eléments, Dept. of Math., Ecole Polytechnique Fédérale de Lausanne, 1973.
[9] P. G. CIARLET and P. A. RAVIART, General Lagrange and Hermite interpolation in \(R^n\) with applications to finite elements methods, Arch. Rational Mech. Anal., 46 (1972), 177-199. Zbl0243.41004 MR336957 · Zbl 0243.41004
[10] G. FICHERA, Linear elliptic differential systems and eigenvalue problems, Lecture Notes in Mathematics 8, Springer, 1965. Zbl0138.36104 MR209639 · Zbl 0138.36104
[11] S. HILBERT, A mollifier useful for approximations in Sobolev spaces and some applications to approximating solutions of differential equations, Math. of Comp., 27 (1973), 81-89.tisf Zbl0257.65087 MR331715 · Zbl 0257.65087
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