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Development of a hierarchical and adaptive finite element software. (English) Zbl 0665.73057

This paper is concerned with the implementation of a discretization error in finite element computations for the analysis of the Navier equations and of the adaptive algorithm it implies. We present the numerical techniques involved using hierarchical finite element formulation.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74-04 Software, source code, etc. for problems pertaining to mechanics of deformable solids
Full Text: DOI

References:

[1] Axelsson, O.; Barker, V. A., Finite Elernent Solution of Boundary Problems (1984), Academic Press: Academic Press New York · Zbl 0537.65072
[2] Babuska, I.; Rheinboldt, W. C., Error estimates for adaptive finite element computations, SIAM J. Numer. Anal., 15, 4 (1984)
[3] Babuska, I.; Rheinboldt, W. C., Adaptive approaches and reliability estimations in finite element analysis, Comput. Methods Appl. Mech. Engrg., 17/18, 519-540 (1979) · Zbl 0396.73077
[4] Bank, R. E.; Sherman, A. H.; Weiser, A., Refinement algorithms and ata structures for regular local mesh refinement, Sci. Comput. (1983)
[5] Bank, R., PLTMG User’s guide, (Technical report (1981), University of California: University of California San Diego) · Zbl 0990.65500
[6] Demkowicz, L.; Oden, J. T.; Strouboulis, T., Adaptive finite elements for flow problems with moving boundaries, Comput. Methods Appl. Mech. Engrg., 46, 217-251 (1984), Part 1 · Zbl 0583.76025
[7] Kelly, D. W.; de S. R. Gago, J. P.; Zienkiewicz, O. C.; Babuska, I., A posteriori error analysis and adaptive processes in the finite element method, Part I. Error analysis, Internat. J. Numer. Methods Engrg., 19, 1593-1619 (1983) · Zbl 0534.65068
[8] Kelly, D. W.; de S. R. Gago, J. P.; Zienkiewicz, O. C.; Babuska, I., A posteriori error analysis and adaptive processes in the finite element method, Part II. Adaptive mesh refinement, Internat. J. Numer. Methods Engrg., 19, 1621-1656 (1983) · Zbl 0534.65069
[9] Rheinboldt, W.; Mesztenyi, C., On a data structure for adaptive finite element mesh refinements, ACM Trans., 6, 2 (1980) · Zbl 0437.65081
[10] Stuben, K.; Trottenberg, U., Multigrid methods: fundamental algorithms, model problem analysis and applications, (Multigrid Methods, Proceedings Köln-Porz Conference (1981), Springer: Springer Berlin), 1-176, 1-176 · Zbl 0505.65035
[11] Zienkiewicz, O. C.; Kelly, D. W., The hierarchical concept in finite element analysis, Comput. Struct., 16, 53-65 (1983) · Zbl 0498.73072
[12] Zienkiewicz, O. C.; Kelly, D. W.; de S. R. Gago, J. P.; Babuska, I., Hierarchical finite element approaches, error estimates and adaptive refinement, MAFELAP, 313-346 (1981) · Zbl 0533.65073
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