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Existence de maillages optimaux dans les méthodes d’éléments finis. (French) Zbl 0447.65062

##### MSC:
 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations
##### Keywords:
error minimization; finite element methods; optimal mesh
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##### References:
 [1] 1 I BABUSKA et W RHEINBOLDT, Analysis of Optimal Finite Element in $$R$$, University of Maryland, Technical note BN-869, 1978 [2] 2 I BABUšKA et W RHEINBOLDT, Error Estimates for Adaptive Finite Element Computations, University of Maryland, Technical note BN-854, 1977, S I A M J Num anal (à paraître) Zbl0398.65069 MR483395 · Zbl 0398.65069 [3] 3 W E CARROLL et R M BARKER, A Theorem of Optimum Finite Element Idealisation, Int J Solids and Structures, vol 9, 1973, p 883-895 MR337119 [4] 4 Ph CIARLET, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978 Zbl0383.65058 MR520174 · Zbl 0383.65058 [5] 5 G M MCNEICE et P V MARCAL, Optimization of Finite Element Grids Based on Minimum Potential Energy, J Engg for Industry, vol 95, série B, n^\circ 1, 1973, p 186-190 [6] 6 J NEČAS, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967 MR227584 · Zbl 1225.35003 [7] 7 P OLIVEIRA, Maillages optimaux dans les méthodes d’éléments finis, Thèse de 3e cycle, Paris, 1979 [8] 8 P OLIVEIRADérivabilité de l’erreur par rapport à la triangulation dans les méthodes d’éléments finis R A I R O , Analyse numérique, vol 14, n^\circ 3 1980 Zbl0447.65063 · Zbl 0447.65063 [9] 9 W PRAGER, A Note on the Optimal Choice of Finite Elements Grids, Computer Methods in Applied Mechanics and Engineering, vol 6, 1975, p 363-366 Zbl0323.73059 MR458944 · Zbl 0323.73059 [10] 10 J W TANG et D J TURCKE, Characteristics of Optimal Grids, Computer Methods in Applied Mechanics and Engineering, vol 11, 1977, p 31-37 [11] 11 D J TURCKE et G M MCNEICE, Guidelines for Selecting Finite Element Grids Based on an Optimization Study, Computers and Structures, vol 4, 1974, p 499-519
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