Abstract
In this paper, a general class of h methods for adaptive finite element approximations is described that has been applied successfully to three classes of problems in solid and fluid mechanics:
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(1)
supersonic flow of compressible gases in two-dimensional domains;
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(2)
flow interaction in supersonic rotor-stator simulations;
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(3)
quasi-static problems in viscoplasticity of metals under elevated temperatures.
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References
J.T. Oden, T. Strouboulis, and P. Devloo, “Adaptive finite element methods for the analysis of inviscid compressible flow, I: Fast refmement/unrefinement and moving mesh methods for unstructured meshes,” Comput. Methods Appl. Mech. Engrg., 59, No. 3 (1986), 327 – 362.
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J.M. Bass and J.T. Oden, “Adaptive finite element methods for a class of evolution problems in viscoplasticity,” Internat. J. Engrg. Sci., 25, No. 6 (1987), 623 – 653.
J.T. Oden, T. Strouboulis, and P. Devloo, “Adaptive finite element methods for compressible flow problems,” in Numerical Methods for Compressible Flows— Finite Difference, Element and Volume Techniques(T.E. Tezduyor and T.J.R. Hughes, eds.), AMD Vol. 78, ASME, New York, 1987, pp. 115 – 126.
L. Demkowicz and J.T. Oden, “An adaptive characteristic Petrov—Galerkin finite element method for linear and nonlinear convection-dominated diffusion problems in one space variable,” J. Comput. Physics, 68, No. 1, (1986), 188 – 273.
T. Strouboulis, P. Devloo, and J.T. Oden, “A moving-grid finite element algorithm for supersonic flow interaction between moving bodies,” Comput. Methods Appl. Mech. Engrg., 59, No. 2, (1986), 235 – 255.
J.T. Oden and L. Demkowicz, “Advances in adaptive improvements,” in State of the Art Surveys in Computational Mechanics, Special Publications, American Society of Mechanical Engineers, New York, to appear.
J.T. Oden, L. Demkowicz, T. Strouboulis, and P. Devloo, “Adaptive methods for problems in solid and fluid mechanics,” in Accuracy Estimates and Adaptive Refinements in Finite Element Computations, ( I. Babuska, O.C. Zienkiewicz, J. Gago, and E.R. Arantes Oliveira, eds.), Wiley, Chichester, 1986.
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Oden, J.T. (1988). Adaptive Finite Element Methods for Problems in Solid and Fluid Mechanics. In: Dwoyer, D.L., Hussaini, M.Y., Voigt, R.G. (eds) Finite Elements. ICASE/NASA LaRC Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3786-0_12
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DOI: https://doi.org/10.1007/978-1-4612-3786-0_12
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