Abstract
Techniques for error estimation have recently been developed for stress analysis problems. These methods may be considered as optimizing the finite element analysis according to the intrinsic behaviour of the given problem. This type of error estimation is now applied to heat flow analyses. The technique will first be demonstrated for steady state thermal problems and then extended to transient problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
I. Babuska and W.C. Rheinboldt. Adaptive approaches and reliability estimates in finite element analysis. Computer Methods in Applied Mechanics and Engineering, 17 /18: 519–514, 1979.
I. Babuska and W.C. Rheinboldt. Error estimates for adaptive fi-nite element computations. SIAM Journal of Numerical Analysis, 15, 1978.
D.W. Kelly, J.P. De S.R. Gago, O.C. Zienkienwicz, and I. Babuska. A posteriori error analysis and adaptive processes in the finite element method: part 1 — error analysis. International Journal for Numerical Methods in Engineering, 19: 1596–1619, 1983.
J.P. De S.R. Gago, D.W. Kelly, O.C. Zienkienwicz, and I. Babuska. A posteriori error analysis and adaptive processes in the finite element method: part 2 — adaptive mesh refinement. International Journal for Numerical Methods in Engineering, 19: 1621–1656, 1983.
J. Peraire, M. Vahdati, K. Morgan, and O.C. Zienkiewicz. Adaptive remeshing for compressible flow computations. Journal of Computational Physics, 72: 449–466, 1987.
J. Peraire, K. Morgan, and J. Piero. Unstructured finite element mesh generation and adaptive procedures for CFD. In AGARD FDP: Specialists meeting, Loen, Norway, May 1989.
O.C. Zienkiewicz, Y.C. Liu, and G.C. Huang. Error estimates and convergence rates for various incompressible elements. International Journal for Numerical Methods in Engineering, 28: 2191–2202, 1989.
H.C.Huang and R.W.Lewis. Adaptive analysis for heat flow problems using error estimation techniques. In Sixth International Conference for Numerical Methods in Thermal Problems, Swansea, U.K., July 1989. Pineridge Press, Swansea.
O.C. Zienkiewicz and J.Z. Zhu. A simple error estimator and adaptive procedure for practical engineering analysis. International Journal for Numerical Methods in Engineering, 24: 337–357, 1987.
E. Hinton and J.S. Campbell. Local and global smoothing of discontinuous finite element functions using a least squares method. International Journal for Numerical Methods in Engineering, 8: 461–480, 1974.
T.J.R.Hughes. The Finite Element Method - Linear Static and Dynamic Finite Element Analysis. Prentice-Hall International, Inc., Englewood Cliffs, New Jersey 07632, 1987.
M. Zlamal. Superconvergence and reduced integration in the finite element method. Mathematics of Computation, 32: 663–685, 1978.
O.C. Zienkiewicz and J.Z. Zhu. Adaptivity and mesh generation. International Journal for Numerical Methods in Engineering, 32: 783–810, 1991.
R.W. Lewis, H.C. Huang, A.S. Usmani, and J.T. Cross. Finite element analysis of heat transfer and flow problems using adaptive remeshing including application to solidification. International Journal for Numerical Methods in Engineering, 1991. To be published in a special issue on adaptivity and meshing.
J. Barlow and G.A.O. Davies. Selected FE benchmarks in structural and thermal analysis. Technical Report FEBSTA REV 1, NAFEMS, 1986.
H.S. Carslaw and J.C. Jaeger. Conduction of Heat in Solids. Clarendon Press, Oxford, 1959.
P.A.B. de Sampaio, P.R.M. Lyra, K. Morgan, and N.P. Weatherill. Petrovgalerkin solutions of the incompressible Navier-Stokes equations in primitive variables with adaptive remeshing. Technical Report CR/701/92, Department of Civil Engineering, University College of Swansea, 1992.
O.C. Zienkiewicz and J.Z. Zhu. The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique, Part 2: Error estimates and adaptivity. International Journal for Numerical Methods in Engineering, 33: 1331–1382, 1992.
A. Tessler, H.R. Riggs, and S.C. Macy. A variational method for finite element stress recovery and error estimation. Computer Methods in Applied Mechanics and Engineering, 111: 369–382, 1994.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag London Limited
About this chapter
Cite this chapter
Huang, HC., Usmani, A.S. (1994). Adaptive Heat Transfer Analysis. In: Finite Element Analysis for Heat Transfer. Springer, London. https://doi.org/10.1007/978-1-4471-2091-9_6
Download citation
DOI: https://doi.org/10.1007/978-1-4471-2091-9_6
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2093-3
Online ISBN: 978-1-4471-2091-9
eBook Packages: Springer Book Archive