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Diaz, Alejandro R.; Kikuchi, Noboru; Taylor, John E.

A method of grid optimization for finite element methods. (English) Zbl 0509.73071

Comput. Methods Appl. Mech. Eng. 41, 29-45 (1983).
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Cited in 1 Review
Cited in 27 Documents

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74S99 Numerical and other methods in solid mechanics
74P99 Optimization problems in solid mechanics
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs

Keywords:

grid optimization; measure of interpolation error; changing location of nodes within fixed number of degrees of freedom; examples
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\textit{A. R. Diaz} et al., Comput. Methods Appl. Mech. Eng. 41, 29--45 (1983; Zbl 0509.73071)
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References:

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[2] Babuska, I.; Rheinboldt, W.C., Analysis of optimal finite-element meshes in R1, Math. comput., 33, 435-463, (1979) · Zbl 0431.65055
[3] Babuska, I.; Rheinboldt, W.C., Reliable error estimation and mesh adaptation for the finite element method, (), 67-108
[4] Babuska, I.; Szabo, B., On the rates of convergence of the finite element method, Internat. J. numer. meths. engrg., 18, 323-341, (1982) · Zbl 0498.65050
[5] Sewell, G., An adaptive computer program for the solution of DIV(P(X, Y)GRADU)= F(X, Y, U) on a polygonal region, (), MAFELAP 1975
[6] Zienkiewicz, O.C.; Kelly, D.W.; Gago, J.P.de S.R.; Babuska, I., Hierarchical finite element approaches, error estimates and adaptive refinement, () · Zbl 0498.73072
[7] Zienkiewicz, O.C.; Gago, J.P.de S.R.; Kelly, D.W., The hierarchical concept in finite element analysis, Comput. & structures, 16, 53-65, (1983) · Zbl 0498.73072
[8] Peano, A.G., Hierarchies of conforming finite elements for plane elasticity and plate bending, Comput. math. appl., 2, 221-224, (1976) · Zbl 0369.73071
[9] Szabo, B.A.; Mehta, A.K., p-convergent finite element approximations in fracture mechanics, Internat. J. numer. meths. engrg., 12, 551-560, (1978) · Zbl 0369.73097
[10] e Oliveira, E.R.de Arantes, Optimization of finite element solutions, ()
[11] Turcke, D.J.; McNeice, G.M., Guidelines for selecting finite element grids based on an optimization study, Comput. & structures, 4, 499-519, (1974)
[12] Turcke, D.J., Characteristics of piecewise approximation in numerical analysis, (), 15-26
[13] Felippa, C.A., Optimization of finite element grids by direct energy search, Appl. math. modelling, 1, 93-96, (1976) · Zbl 0348.65094
[14] Felippa, C.A., Numerical experiments in finite element grid optimization by direct energy search, Appl. math. modelling, 1, 239-244, (1977)
[15] Melosh, R.J.; Marcal, P.V., An energy basis for mesh refinement of structural continua, Internat. J. numer. meths. engrg., 11, 1083-1091, (1977) · Zbl 0359.73065
[16] Shephard, M.S.; Gallagher, R.H.; Abel, J.F., The synthesis of near-optimum finite element meshes with iteractive computer graphics, Internat. J. numer. meths. engrg., 15, 1021-1039, (1980) · Zbl 0443.73060
[17] Shephard, M.S., Finite element grid optimization—a review, (), 1-14
[18] Ciarlet, P.G., The finite element method for elliptic problems, (1978), North-Holland Amsterdam · Zbl 0445.73043
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.