[1] |
Babuska, I.; Szabo, B., On the rates of convergence of the finite element method, Int. J. Numer. Methods Eng., 20, 323-341 (1982) · Zbl 0498.65050 · doi:10.1002/nme.1620180302 |
[2] |
Blacker, T.; Belytschko, T., Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements, Int. J. Numer. Methods Eng., 37, 517-536 (1994) · Zbl 0789.73064 · doi:10.1002/nme.1620370309 |
[3] |
Blacker, T.; Stevenson, M., Paving: a new approach to automated quadrilateral mesh generation, Int. J. Numer. Methods Eng., 32, 811-847 (1991) · Zbl 0755.65111 · doi:10.1002/nme.1620320410 |
[4] |
Blum, H.; Wathen-Dunn, W., A transformation for extracting new descriptors of shape, Models for the perception of speech and visual form (1967), Cambridge, MA: MIT Press, Cambridge, MA |
[5] |
Blum, H., Biological shape and visual science, J. Theor. Biol., 38, 205-287 (1973) · doi:10.1016/0022-5193(73)90175-6 |
[6] |
Blum, H.; Nagel, R., Shape description using weighted symmetric axis features, Pattern Recogn., 10, 167-180 (1973) · Zbl 0379.68067 · doi:10.1016/0031-3203(78)90025-0 |
[7] |
Bookstein, F. L., The line skeleton, Comput. Graphics Image Process, 11, 123-137 (1979) · doi:10.1016/0146-664X(79)90062-5 |
[8] |
Botkin, M. A.; Bennet, J. A.; Babuska, I.; Gago, J. P.; Zienkiewicz, O. C.; Kelly, D. W., The application of adaptive mesh refinement to shape optimization of plate structures, Accuracy estimates and adaptive refinements in finite element computations, 227-246 (1986), New Delhi: John Wiley, New Delhi |
[9] |
Buell, W. R.; Bush, B. A., Mesh generation — a survey, J. Eng. Ind., ASME, 7, 332-338 (1973) |
[10] |
Bugeda G, Oliver J 1991 Automatic adaptive remeshing for structural shape optimization.European Conf. on New Advances in Computat. Struct. Mech. Giens, France · Zbl 0850.73209 |
[11] |
Calabi, L.; Hartnett, W. E., A theorem for closed non convex sets, Proc. Am. Math. Soc., 19, 1495-1498 (1968) · Zbl 0172.24102 · doi:10.2307/2036239 |
[12] |
Calabi, L.; Hartnett, W. E., Shape recognition, prairie fires, convex deficiencies and skeletons, Am. Math. Mon., 75, 335-338 (1968) · Zbl 0161.41602 · doi:10.2307/2313409 |
[13] |
Cantin, G.; Touzot, G.; Loubignac, G., An iterative algorithm to build continuous stress and displacement relations, Int. J. Numer. Methods Eng., 12, 1453-1506 (1978) · Zbl 0434.73087 · doi:10.1002/nme.1620121004 |
[14] |
Cedillo, H. E F.; Bhatti, M. A., A simple strain energy based finite element mesh refinement scheme, Comput. Struct., 28, 523-533 (1988) · Zbl 0629.73057 · doi:10.1016/0045-7949(88)90025-9 |
[15] |
Cook, R. D., Loubignac’s iterative method in finite element elastostatics, Int. J. Numer. Methods Eng., 18, 67-75 (1982) · Zbl 0468.73089 · doi:10.1002/nme.1620180106 |
[16] |
Gago, J. P de S. R.; Kelly, D. W.; Zienkiewicz, O. C.; Babuska, I., A-posteriori error analysis and adaptive processes in the finite element method: Part II — adaptive mesh refinement, Int. J. Numer. Methods Eng., 19, 1621-1656 (1983) · Zbl 0534.65069 · doi:10.1002/nme.1620191104 |
[17] |
Grosse, I. R.; Katragadda, P.; Benoit, J., An adaptive accuracy-baseda posteriori error estimator, Finite Elements Anal. Design, 12, 75-90 (1992) · Zbl 0766.73062 · doi:10.1016/0168-874X(92)90008-Z |
[18] |
Gursoy, H. N.; Patrikalakis, N. M., An automatic coarse and fine surface mesh generation scheme based on medial axis transform: Part 1. Algorithms, Eng. Comput., 8, 121-137 (1992) · Zbl 0757.65119 · doi:10.1007/BF01200364 |
[19] |
Heighway, E. A., A mesh generator for automatically subdividing irregular polygons into quadrilaterals, IEEE Trans. Magnetics, 19, 2535-2538 (1983) · doi:10.1109/TMAG.1983.1062810 |
[20] |
Ho-Le, K., Finite element mesh generation methods: A review and classification, Comput. Aided Design., 20, 27-38 (1988) · Zbl 0661.65124 · doi:10.1016/0010-4485(88)90138-8 |
[21] |
Kelly, D. W., The self equilibration of residuals and complimentary a-posteriori error estimates in FEM, Int. J. Numer. Methods Eng., 20, 1491-1506 (1984) · Zbl 0575.65100 · doi:10.1002/nme.1620200811 |
[22] |
Kelly, D. W.; Isles, J. D., A procedure for a-posteriori error analysis for the FEM which contains a bounding measure, Int. J. Numer. Methods Eng., 31, 63-71 (1989) |
[23] |
Kelly, D. W.; Gago, J. P de S. R.; Zienkiewicz, O. C.; Babuska, I., A-posteriori error analysis and adaptive processes in the finite element method: Part I — error analysis, Int. J. Numer. Methods Eng., 19, 1593-1619 (1983) · Zbl 0534.65068 · doi:10.1002/nme.1620191103 |
[24] |
Krishnamoorthy, C. S.; Raphael, B.; Mukherjee, S., Meshing by successive superelement decomposition (MSD) — A new approach to quadrilateral mesh generation, Finite Elements Anal. Design, 20, 1-37 (1995) · Zbl 0875.73296 · doi:10.1016/0168-874X(95)00005-E |
[25] |
Lee, C. K.; Lo, S. H., An automatic adaptive refinement finite element procedure for 2D elastostatic analysis, Int. J. Numer. Methods Eng., 35, 1967-1989 (1992) · Zbl 0775.73273 · doi:10.1002/nme.1620351004 |
[26] |
Lee, D. T., Medial axis transformations of a planar shape, IEEE Trans. Pattern Anal. Mach. Intell., PAMI-4, 363-369 (1982) · Zbl 0483.68085 · doi:10.1109/TPAMI.1982.4767267 |
[27] |
Melosh, R. J.; Marcal, P. V., An energy basis for mesh refinement of structural continua, Int. J. Numer. Methods Eng., 11, 1083-1091 (1977) · Zbl 0359.73065 · doi:10.1002/nme.1620110705 |
[28] |
Montanari, U., A method for obtaining skeleton using a quasi-Euclidian distance, J. Assoc. Comput. Mach., 15, 600-624 (1968) |
[29] |
Mukherjee, S.; Krishnamoorthy, C. S., Adaptive analysis of plates by shear flexible quad4 R-M elements, Finite Elements Anal. Design, 22, 329-366 (1996) · Zbl 0875.73321 · doi:10.1016/0168-874X(96)00024-8 |
[30] |
Mukherjee S, Krishnamoorthy C S 1996b Element patch based enhanced superconvergent stress projection and adaptive finite element analysis.Int. J. Numer. Methods Eng. (communicated) |
[31] |
Nagel R N, Blum H 1976 A symmetric axis basis for object recognition and description.Proc. IEEE meeting on Decision and Control 168-170 |
[32] |
Patrikalakis N M, Gursoy H N 1990 Shape interrogation by medial axis transform. Design Lab Memo, 90-2, Sea Grant College Program, MIT |
[33] |
Reddy, J. M.; Turkiyyah, G., Computation of 3D skeletons using a generalized Delaunay triangulation technique, Comput. Aided Design, 27, 677-694 (1995) · Zbl 0960.68725 · doi:10.1016/0010-4485(94)00025-9 |
[34] |
Talbert, J. A.; Parkinson, AR, Development of an automatic finite element two dimensional mesh generator using quadrilateral elements and Bezier curve boundary definition, Int. J. Numer. Methods Eng., 29, 1551-1567 (1990) · doi:10.1002/nme.1620290712 |
[35] |
Tam, T. K H.; Armstrong, C. G., 2D finite element mesh generation by medial axis subdivision, Adv. Eng. Software, 13, 313-324 (1991) · Zbl 0754.65098 · doi:10.1016/0961-3552(91)90035-3 |
[36] |
Thacker, W. C., A brief review of techniques for generating irregular computational grids, Int. J. Numer. Methods Eng., 15, 1335-1342 (1980) · Zbl 0438.76003 · doi:10.1002/nme.1620150906 |
[37] |
Turkiyyah G, Fenves S J 1988 Generation and interpretation of finite element models in a knowledge based environment. R-90-188, Department of Civil Engineering, Carnegie-Mellon University |
[38] |
Wiberg, N-E; Abdulwahab, F., Patch recovery based on superconvergent derivatives and equilibrium, Int. J. Numer. Methods Eng., 36, 2703-2724 (1993) · Zbl 0800.73463 · doi:10.1002/nme.1620361603 |
[39] |
Wiberg, N-E; Li, X. D., Superconvergent patch recovery of finite element solution and an a-posteroriL_2 norm error estimate, Commun. Numer. Methods Eng., 10, 313-320 (1994) · Zbl 0802.65108 · doi:10.1002/cnm.1640100406 |
[40] |
Wiberg, N-E; Abdulwahab, F.; Ziukas, S., Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions, Int. J. Numer. Methods Eng., 37, 3417-3440 (1994) · Zbl 0825.73777 · doi:10.1002/nme.1620372003 |
[41] |
Wiberg, N-E; Abdulwahab, F.; Ziukas, S., Improved element stress for node and element patches using superconvergent patch recovery, Commun. Numer. Methods Eng., 11, 619-627 (1995) · Zbl 0830.73068 · doi:10.1002/cnm.1640110708 |
[42] |
Zhu, J. Z.; Zienkiewicz, O. C.; Hinton, E.; Wu, J., A new approach to the development of automatic quadrilateral mesh generation, Int. J. Numer. Methods Eng., 32, 849-866 (1991) · Zbl 0755.65118 · doi:10.1002/nme.1620320411 |
[43] |
Zienkiewicz, O. C.; Zhu, J. Z., A simple error estimator and adaptive procedure for practical engineering analysis, Int. J. Numer. Methods Eng., 24, 337-357 (1987) · Zbl 0602.73063 · doi:10.1002/nme.1620240206 |
[44] |
Zienkiewicz, O. C.; Zhu, J. Z., The superconvergent patch recovery and a-posteriori error estimates. Part 1: The recovery technique, Int. J. Numer. Methods Eng., 33, 1331-1364 (1992) · Zbl 0769.73084 · doi:10.1002/nme.1620330702 |
[45] |
Zienkiewicz, O. C.; Zhu, J. Z., The superconvergent patch recovery and a-posteriori error estimates. Part 2: Error estimates and adaptivity, Int. J. Numer. Methods Eng., 33, 1365-1382 (1992) · Zbl 0769.73085 · doi:10.1002/nme.1620330703 |