A finite element program with h-type mesh adaptation is developed and several test cases for heat transfer, fluid mechanics and structural mechanics are selected for code validations. The element division method is used because of its advantage of avoiding overly twisted elements during mesh refinement and recovery. The adaptive mesh is refined only in the localization region where the feature gradient is high. The overall mesh refinement and the h-adaptive mesh refinement are justified with respect to the computational accuracy and the CPU time cost. Both can improve the computational accuracy. The overall mesh refinement causes the CPU time to greatly increase. However, the CPU time does not increase very much with the increase of the level of h-adaptive mesh refinement. The CPU time cost can be saved using the developed program by orders of magnitude, especially for the system with a large number of elements and nodes.

1.
Zienkiewicz, O. C., and Taylor, R. L., The Finite Element Method, Fifth edition, Volume 1: The Basis, Butterworth-Heinemann, Oxford, 2000.
2.
Zienkiewicz, O. C., and Taylor, R. L, The Finite Element Method, Fifth edition, Volume 2: Solid Mechanics, Butterworth-Heinemann, Oxford, 2000.
3.
Zienkiewicz, O. C., and Taylor, R. L., The Finite Element Method, Fifth edition, Volume 3: Fluid Dynamics, Butterworth-Heinemann, Oxford, 2000.
4.
Johnson
C.
, and
Hansbo
P.
,
1992
, “
Adaptive finite-element methods in computational mechanics
,”
Computer Methods in Applied Mechanics and Engineering
,
101
(
1–3)
, pp.
143
181
.
5.
Tabarraei
A.
, and
Sukumar
N.
,
2005
, “
Adaptive computations on conforming quadtree meshes
,”
Finite Elements in Analysis and Design
,
41
(
7–8)
, pp.
686
702
.
6.
Oden, J. T., and Demkowicz, L., 1989, “A survey of adaptive finite element methods in computational mechanics,” State-of-the-Art Surveys on Computational Mechanics, ASME, NY.
7.
Schwab, Ch., p-and hp-Finite Element Methods: Theory and Applications in Solid and Fluid Mechanics, Oxford, UK, 1998.
8.
Silva
R. C. C.
,
Landau
L.
,
Ribeiro
F. L. B.
,
2000
, “
Visco-plastic h-adaptive analysis
,”
Computers and Structures
,
78
(
1–3)
, pp.
123
131
.
9.
Capon, P., and Jimack, P. K., 1995, “An adaptive finite element method for the compressible Navier-Stokes equations,” Numerical Methods for Fluid Dynamics V, Oxford University Press, New York, NY, pp. 327–333.
10.
Gallimard
L.
,
Ladeveze
P.
, and
Pelle
J. P.
,
1996
, “
Error estimation and adaptivity in elastoplasticity
,”
International Journal for Numerical Methods in Engineering
,
39
(
2)
, pp.
189
217
.
11.
Ainsworth, M., and Oden, J. T., A posteriori error estimation in finite element analysis, Wiley, New York, 2000.
12.
Huerta
A.
,
Rodriguez-Ferran
A.
,
Diez
P.
, and
Sarrate
J.
,
1999
, “
Adaptive finite element strategies based on error assessment
,”
International Journal for Numerical Methods in Engineering
,
46
(
10)
, pp.
1803
1818
.
13.
Zienkiewicz
O.
, and
Zhu
J.
,
1987
, “
A simple error estimator and adaptive procedure for practical engineering analysis
,”
International Journal of Numerical Methods in Engineering
,
24
, pp.
337
357
.
14.
Taylor, H. M., and Karlin, S., An Introduction to Stochastic Modeling, Academic Press, San Diego, CA, 1994.
15.
Beer, G., and Waston, J. O., Introduction to Finite Element and Boundary Element Methods for Engineers, John Wiley & Sons, New York, NY, 1992.
16.
Chandrupatla, T. R., and Belegunda, A. D., Introduction to finite elements in engineering, Second Edition, Prentice-Hall, Upper Saddle River, NJ, 1997.
17.
Huebner, K. H., Dewhirst, D. L., Smith, D. E., and Byrom, T. G., The Finite Element Method for Engineers, Fourth Edition, John Wiley & Sons, New York, NY, 2001.
18.
Carey, G. F., Computational Grids, Generation, Adaptation, and Solution Strategy, Taylor and Francis, Washington D. C., 1997.
19.
Babus˜ka, I., and Rheinboldt, W. C., Reliable error estimation and mesh adaptation for the finite element method, in: J. Oden (Ed.), Computational Methods in Nonlinear Mechanics, North-Holland, Amsterdam, The Netherlands, 1980, pp. 67–108.
20.
Timoshenko, S. P., and Goodier, J. N., Theory of Elasticity, (3rd edition). McGraw-Hill: New York, 1970.
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