References
- Babuska, I. and Rheinboldt, W.C. (1978), "A posteriori error estimates for the finite element method", Int. J. Num. Meth. Engng., 12, 1597-1615. https://doi.org/10.1002/nme.1620121010
- Babuska, I. and Yu, D. (1986), "Asymptotically exact a posteriori error estimator for biquadratic elements", Technical Note BN-1050, Institute for Physical Science and Technology, University of Maryland.
- Babuska, I., Strouboulis, T. and Upadhyay, C.S. (1994), "A model study of the quality of a posteriori error estimators for linear elliptic problems, Error estimation in the interior of patchwise uniform grids of triangles", Comput. Meth. Appl. Mech. Eng., 114, 307-378. https://doi.org/10.1016/0045-7825(94)90177-5
- Babuska, I., Strouboulis, T., Upadhyay, C.S., Gangaraj, S.K. and Copps, K. (1994), "Validation of a posteriori error estimators by numerical approach", Int. J. Num. Meth. Engng., 37, 1073-1123. https://doi.org/10.1002/nme.1620370702
- Baehmann, P.L., Shephard, M.S. and Flaherty, E.J. (1990), "A posteriori error estimation for triangular and tetrahedral quadratic elements using interior residuals", SCOREC Report, Scientific Computation Research Center, Rensselaer Polytechnic Institute.
- Barlow, J. (1976), "Optimal stress locations in the finite element method", Int. J. Num. Meth. Engng., 10, 243-251. https://doi.org/10.1002/nme.1620100202
- Cantin, G., Loubignac, G. and Touzot, G. (1978), "An iterative algorithm to build continuous stress and displacement solutions", Int. J. Num. Meth. Engng., 12, 1493-1506. https://doi.org/10.1002/nme.1620121004
- Cho, J.R and Oden, J.P. (1996), "A priori error estimations of hp - finite element approximations for hierarchical models of plate and shell like structures", Comp. Meth. Appl. Mech. Eng., 132, 135-177. https://doi.org/10.1016/0045-7825(95)00985-X
- Cook, R.D., Malkus, S.D. and Plesha, M.E. (1989), Concepts and Applications of Finite Element Analysis, 3th ed. John Wiley, New York.
- Cugnon, F. and Beckers, P. (1998), "Error estimation for h- and p-method", 8th Mechanical Engineering Chilean Congress 183-188, 27-30 October.
- Dutta, A. and Ramakrishnan, C.V. (1997), "Error estimation in finite element transient dynamic analysis using modal superposition", Engineering Computation, 14, 135-158. https://doi.org/10.1108/02644409710157668
- Hinton, E. and Campbell, J.S. (1974), "Local and global smoothing of discontinuous finite element functions using a least squares method", Int. J. Num. Meth. Engng., 8, 461-480. https://doi.org/10.1002/nme.1620080303
- Hinton, E., Rock, T. and Zienkiewicz, O.C. (1976), "A note on mass lumping and related processes in the finite element method", Int. J. Earth. Engng. Struct. Dyn., 4, 245-249. https://doi.org/10.1002/eqe.4290040305
- Hinton, E., Ozakca, M. and Rao, N.V.R. (1991), "An integrated approach to structural shape optimisation of linearly elastic structures Part 2: shape definition and adaptivity", Computing Systems in Engineering, 2, 27-56. https://doi.org/10.1016/0956-0521(91)90037-6
- Hinton, E., Özakça, M. and Rao, N.V.R. (1991), "Adaptive analysis of thin shells using facet elements", Int. J. Num. Meth. Engng., 32, 1283-1301. https://doi.org/10.1002/nme.1620320608
- Kelly, D.W., Gago, J.P. de S.R. and Zienkiewicz, O.C. (1983), "A posteriori error analysis and adaptive processes in the finite element method, Part I: error analysis", Int. J. Num. Meth. Engng., 19, 1593-1619. https://doi.org/10.1002/nme.1620191103
- Mathisen, K.M and Okstad, K.M. (1999), "Error estimation and adaptivity in explicit nonlinear finite element simulation of quasi-static problems", Comput. Struct., 72 , 627-644. https://doi.org/10.1016/S0045-7949(98)00328-9
- Moan, T. (1974), "Optimal polynomials and 'best' numerical integration formulas on a triangle", ZAMM, 54, 501-508. https://doi.org/10.1002/zamm.19740540706
- Onate, E., Castro, J. and Kreiner, R. (1992), "Error estimation and mesh adaptivity techniques for plate and shell problems", Proc. of the Third Int. Conf. on Quality Assurance and Standards in Finite Element Analysis, 1-17.
- Ozakca, M. (1993), "Analysis and optimal design of structures with adaptivity", Ph.D thesis, C/Ph/168/93, Dept. of Civil Engineering, University College of Swansea, Swansea, UK.
- Peraire, J., Vahdati, M., Morgan, K. and Zienkiewicz, O.C. (1987), "Adaptive remeshing for compressible flow computations", J. Comp. Phys., 72, 449-466. https://doi.org/10.1016/0021-9991(87)90093-3
- Robinson, D.J. and Armstrong, C.G. (1992), "An experimental comparison of energy error estimators for 8-noded isoparametric quadrilateral elements", Proc. of the Third Int. Conf. on Quality Assurance and Standards in Finite Element Analysis, NAFEM, 202-212.
- Shephard, M.S., Niu, Q.X. and Baehmann, P.L. (1989), "Some results using stress projectors for error indication and estimation", SCOREC Report, Scientific Computation Research Center, Rensselaer Polytechnic Institute.
- Sienz, J. (1994), "Integrated structural modelling, adaptive analysis and shape optimization", Ph.D. thesis, C/M/ 259/90, Dept. of Civil Eng. University College of Swansea.
- Stephen, D.B and Steven, G.P. (1997), "Natural frequency error estimation using a path recovery technique", J. Sound Vib., 200, 151-165. https://doi.org/10.1006/jsvi.1996.0658
- Strouboulis, T. and Haque, K.A. (1992), "Recent experiences with error estimation and adaptivity, Part 2: error estimation for h - adaptive approximations on grids of triangles and quadrilaterals", Comp. Meth. Appl. Mech. Engng., 100, 359-430. https://doi.org/10.1016/0045-7825(92)90090-7
- Zienkiewicz, O.C. and Zhu, J.Z. (1992), "The superconvergent patch recovery and a posteriori error estimates. Parts 1-2", Int. J. Num. Meth. Engng., 33, 1331-1382. https://doi.org/10.1002/nme.1620330702
- Zienkiewicz, O.C., Liu, Y.C. and Huang, G.C. (1988), "An error estimate and adaptive refinement method for extrusion and other forming problems", Int. J. Num. Meth. Engng., 25, 23-42. https://doi.org/10.1002/nme.1620250105
- Zienkiewicz, O.C. and Taylor, R.L. (2000), The Finite Element Method, 5th ed., Vols. 1-3, Butterworth Heinemann, London.
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