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On Jirousek method and its generalizations

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Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Konferencja
International Workshop on the Trefftz Method (2 ; 1999 ; Lisbon, Portugal)
Języki publikacji
EN
Abstrakty
EN
Professor Jirousek has been a very important driving force in the modern development of Trefftz method, contributing to its application in many different fields such as elasticity, shells and plates theory, Poisson equation and transient heat analysis. This article is dedicated to him. The focus of the paper is to incorporate Jirousek method into a very general framework of Trefftz method which has been introduced by Herrera. Usually finite element methods are developed using splines, but a more general point of view is obtained when they are formulated in spaces of fully discontinuous functions - i.e., spaces in which the functions together with their derivatives may have jump discontinuities - and in the general context of boundary value problems with prescribed jumps. Two broad classes of Trefftz methods are obtained: direct (Trefftz-Jirousek) and indirect (Trefftz-Herrera) methods. In turn, each one of them can be divided into overlapping and non-overlapping.
Słowa kluczowe
Rocznik
Strony
325--342
Opis fizyczny
Bibliogr. 74 poz., rys.
Twórcy
autor
  • Instituto de Investigationes en Matematicas Aplicadas y en Sistemas, Universidad Nacional Autonoma de Mexico, 22-582, 14000, Mexico, D. F.
Bibliografia
  • [1] M.B. Allen, I. Herrera, and G.F. Pinder. Numerical modeling in science and engineering. John Wiley & Sons, 1988. 418 pp.
  • [2] H. Begehr and R.P. Gilbert. Transformations, transmutations, and Kernel Functions, volume 1. Longman Scientific & Technical, 1992.
  • [3] S. Bergman. Integral operators in the theory of linear partial dierential equations, volume 23. Ergeb. Math. Grenzgeb, 2, rev. print. Springer, Berlin, 1969
  • [4] R. Berlanga and I. Herrera. The Gauss theorem for domain decompositions in Sobolev spaces. Applicable Analysis: An International Journal. (in press).
  • [5] M. Celia and I. Herrera. Solution of general differential equations using the algebraic theory approach. Numerical Methods for Partial Differential Equations, 3(1):117-129, 1987.
  • [6] M. Celia, I. Herrera, E. Bouloutas, and J. S. Kindred. A new numerical approach for the advective diffusive transport equation. Numerical Methods for Partial Differential Equations, 5(3):203-226, 1989.
  • [7] M.A. Celia, T. F. Russell, I. Herrera, and R.E. Ewing. An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation. Advances in Water Resources, 13(4):187-206, 1990.
  • [8] T. F. Chan, R. Glowinski, J. Périaux, and O.B. Widlund, editors. Domain Decomposition Methods. Proceedings of the Second International Symposium on Domain Decomposition Methods, Los Angeles, California, 1989. SIAM, Philadelphia.
  • [9] T. F. Chan, R. Glowinski, J. Périaux, and O.B. Widlund, editors. Domain Decomposition Methods for Partial Differential Equations. Proceedings of the Third International Symposium on Domain Decomposition Methods, Houston, Texas, 1990. SIAM, Philadelphia.
  • [10] D.L. Colton. Partial differential equations in the complex domain. Pitman, London, 1976.
  • [11] D.L. Colton. Solution of boundary value problems by the method of integral operators. Pitman, London, 1976.
  • [12] D.L. Colton. Analytic theory of partial differential equations, volume XII. Pitman, Boston, 1980.
  • [13] R.P. Gilbert. Function theoretic methods in partial differential equations, volume XVIII. Academic Press, New York, 1969.
  • [14] R.P. Gilbert. Constructive methods for elliptic partial differential equations. Lecture Notes in Math., VII(365):397, 1974.
  • [15] R. Glowinski, G.H. Golub, and J. Périaux, editors. Domain Decomposition Methods for Partial Differential Equations. Proceedings of the First International Symposium on Domain Decomposition Methods, Paris, France, 1988. SIAM, Philadelphia.
  • [16] R. Glowinski, Y.A. Kuznetsov, G. Meurant, and J. Périaux, editors. Domain Decomposition Methods for Partial Differential Equations. Proceedings of the Fourth International Symposium on Domain Decomposition Methods, Moscow, 1991. SIAM, Philadelphia.
  • [17] R. Glowinski and A. Lichnewsky, editors. Computing Methods in Applied Sciences and Engineering. Proceedings of the Ninth International Conference on Computing Methods in Applied Sciences and Engineering, Paris, France, 1990. SIAM, Philadelphia.
  • [18] H. Gourgeon and I. Herrera. Boundary methods. Complete systems for biharmonic equations. In C.A. Brebbia, editor, Boundary Element Methods, pages 431-441. Springer Verlag, Berlin, 1981.
  • [19] G. Herrera and I. Herrera. An Eulerian-Lagrangian method of cells, based on localized adjoint methods. Numerical Methods for Partial Differential Equations, 10:205-223, 1994.
  • [20] I. Herrera. Boundary methods. A criterion for completeness. Proceedings National Academy of Sciences, U.S.A., 77(8):4395-4398, 1980.
  • [21] I. Herrera. An algebraic theory of boundary value problems. KINAM, 3(2):161-230, 1981.
  • [22] I. Herrera. Boundary methods for fluids. In R.H. Gallagher, D. Norrie, J.T. Oden, and O.C. Zienkiewicz, editors, Finite Elements in Fluids, volume IV, chapter 19, pages 403-432. John Wiley & Sons Ltd., 1982.
  • [23] I. Herrera. Boundary methods. An algebraic theory. Advanced Publishing Program. Pitman, Boston, London, Melbourne, 1984.
  • [24] I. Herrera. Trefftz method. In C.A. Brebbia, editor, Topics in boundary element research. Basic Principles and Applications, volume 1, chapter 10, pages 225-253. Springer Verlag, 1984.
  • [25] I. Herrera. Unified approach to numerical methods. Part 1: Green's formulas for operators in discontinuous fields. Numerical Methods for Partial Differential Equations, 1(1):12-37, 1985.
  • [26] I. Herrera. Unified approach to numerical methods. Part 2: Finite elements, boundary methods and its coupling. Numerical Methods for Partial Differential Equations, 1(3):159-186, 1985.
  • [27] I. Herrera. Some unifying concepts in applied mathematics. In R.E. Ewing, K.I. Gross, and C.F. Martin, editors, The Merging of Disciplines: New Directions in Pure, Applied, and Computational Mathematics, pages 79-88. Springer Verlag, New York, 1986.
  • [28] I. Herrera. The algebraic theory approach for ordinary differential equations: highly accurate finite differences. Numerical Methods for Partial Differrential Equations, 3(3):199-218, 1987.
  • [29] I. Herrera. Localized adjoint methods: a new discretization methodology. In W.E. Fitzgibbon and M.F. Wheeler, editors, Computational Methods in Geosciences, chapter 6, pages 66-77. SIAM, 1992.
  • [30] I. Herrera. On operator extensions: the algebraic theory approach. In Advances in Optimization and Numerical Analysis. Proceedings of the VI Workshop on Optimization and Numerical Analysis, Mathematics and its Applications, pages 155-163, Oaxaca, Oax. Mexico, 1992. Kluwer Academic Publishers.
  • [31] I. Herrera. Innovative discretization methodologies based on LAM. In K. Morgan et al., editor, Finite Elements in Fluids: New Trends and Applications, volume 2, pages 1437-1447. Pineridge Press, 1993.
  • [32] I. Herrera. Trefftz{Herrera domain decomposition. Advances in Engineering Software, 24:43-56, 1995. Special Volume on Trefftz Method: 70 Years Anniversary.
  • [33] I. Herrera. Trefftz-Herrera method. CAMES, 4(3/4):369-382, 1997.
  • [34] I. Herrera. Collocation from a broad perspective. Comp. Meths. in Water Resources, 2000. (in press).
  • [35] I. Herrera and R. Berlanga. Operator ext. & Green-Herrera formulas. (in preparation).
  • [36] I. Herrera, R.E. Ewing M.A. Celia, and T. Russell. Eulerian-Lagrangian localized adjoint method: the theoretical framework. Numerical Methods for Partial Differrential Equations, 9(4):431-457, 1993.
  • [37] I. Herrera, L. Chargoy, and G. Alduncin. Unified approach to numerical methods. Part 3: Finite differences and ordinary differential equations. Numerical Methods for Partial Differrential Equations, 1(4):241-258, 1985.
  • [38] I. Herrera and M. Diaz. Indirect methods of collocation: Trefftz{Herrera collocation. Numerical Methods for Partial Differential Equations, 15(6):709-738, 1999.
  • [39] I. Herrera and H. Gourgeon. Boundary methods. Complete systems for Stokes problems. Computer Methods in Applied Mechanics & Engineering, 30:225-241, 1982.
  • [40] I. Herrera and G. Herrera. Collocation: direct methods. (in preparation).
  • [41] J. Jirousek. Basis for development of large finite elements locally satisfying all field equations. Comp. Meth. Appl. Mech. Eng., 14:65-92, 1978.
  • [42] J. Jirousek. Hybrid-Trefftz plate bending elements with p-method capabilities. Int. J. Numer. Meth. Eng., 24:1367-1393, 1987.
  • [43] J. Jirousek and L. Guex. The hybrid-Trefftz finite element model and its application to plate bending. Int. J. Numer. Meth. Eng., 23:651-693, 1986.
  • [44] J. Jirousek and N. Leon. A powerful finite element for plate bending. Comp. Meth. Appl. Mech. Eng., 12:77-96, 1977.
  • [45] J. Jirousek and M. N'Diaye. Solution of orthotropic plates based on p-extension of the hybrid-Trefftz finite element model. Comp. Struct., 34(1):51-62, 1990.
  • [46] J. Jirousek and Q. H. Qin. Application of hybrid-Trefftz element approach to transient heat conduction analysis. Comput. Struct., 58:195-201, 1994.
  • [47] J. Jirousek, B. Szybinski, and A. Wroblewski. Mesh design and reliability assurance in hybrid-Trefftz p-element approach. Analysis and Design, 1996.
  • [48] J. Jirousek and P. Teodorescu. Large finite elements method for the solution of problems in the theory of elasticity. Comp. Struct., 15(5):575-587, 1982.
  • [49] J. Jirousek and A. Venkatesh. Implementation of curvilinear geometry into p-version HT plate elements. Int. J. Numer. Meth. Eng., 28(431-443), 1989.
  • [50] J. Jirousek and A. Venkatesh. A simple stress error estimator for hybrid-Trefftz p-version elements. Int. J. Numer. Meth. Eng., 28:211-236, 1989.
  • [51] J. Jirousek and A. Venkatesh. Adaptivity in hybrid-Trefftz finite element formulation. Int. J. Numer. Meth. Eng., 29:391-405, 1990.
  • [52] J. Jirousek and A. Venkatesh. A new FE approach for adaptive reliability assurance. Computers & Structures, 37:217-230, 1990.
  • [53] J. Jirousek and A. Wroblewski. T-elements: state of the art and future trends. Archives of Computational Methods in Engineering, 3(4):323-434, 1996.
  • [54] J. Jirousek, A. Wroblewski, Q. Qin, and X. He. A family of quadrilateral hybrid-Trefftz p-elements for thick plate analysis. Comp. Meth. Appl. Mech. Eng., 127:315-344, 1995.
  • [55] J. Jirousek, A. Wroblewski, and B. Szybinski. A new 12DOF quadrilateral element for analysis of thick and thin plates. Int. J. Numer. Meth. Eng., 38:2619-2638, 1995.
  • [56] J. Jirousek and A.P. Zielinski. Survey of Trefftz-type element formulations. Computers and Structures, 63(2):225-242, 1997.
  • [57] D.E Keyes, T.F. Chan, G. Meurant, J. S. Scroggs, and R.G. Voigt, editors. Domain Decomposition Methods for Partial Differential Equations. Proceedings of the Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, Norfolk, Virginia, 1992. SIAM, Philadelphia.
  • [58] D.E. Keyes and J. Xu, editors. Domain Decomposition Methods in Scientific and Engineering Computing. Proceedings of Seventh International Conference on Domain Decomposition, Providence, Rhode Island, 1994. The Pennsylvania State University, AMS.
  • [59] M. Kracht and E. Kreyszig. Methods of complex analysis in partial differential equations with applications. Wiley & Sons, New York, 1988.
  • [60] E. Lanckau. Complex integral operators in mathematical physics. Akademie-Verlag Berlin. to appear.
  • [61] P.L. Lions. On the Schwarz alternating method. In R. Glowinski et al, editor, First International Symposium on Domain Decomposition Methods for Partial Differential Equations, pages 1-42, 1987.
  • [62] L. Loomis and S. Sternberg. Advanced Calculus. Addison-Wesley, Reading, Mass., 1968.
  • [63] P. Petrolito. Hybrid-Trefftz quadrilateral elements for thick plate analysis. Comp. Meth. Appl. Mech. Eng., 78:331-351, 1990.
  • [64] R. Piltner. On the representation of three-dimensional elasticity solutions with the aid of complex valued functions. J. Elast., 22:45-55, 1989.
  • [65] R. Piltner. A quadrilateral hybrid-Trefftz plate bending element for the inclussion of warping based on a three-dimensional plate formulation. International Journal for Numerical Methods in Engineering, 33:387-408, 1992.
  • [66] A. Quarteroni, J. Périaux, Y. A. Kuznetsov, and O. B. Widlund, editors. Domain Decomposition Methods in Science and Engineering. Proceedings of the Sixth International Conference on Domain Decomposition, Como, Italy, 1994. AMS, Providence, Rhode Island.
  • [67] F.J. Sanchez Sesma, I. Herrera, and J. Aviles. A boundary method for elastic wave diffraction. application to scattering of sh-waves by surface irregularities. Bulletin of the Seismological Society of America, 72(2):473-490, 1982.
  • [68] E. Trefftz. Ein Gegenstück zum Ritzschen Verfahren. In Proceedings 2nd International Congress of Applied Mechanics, pages 131-137, Zurich, 1926.
  • [69] I.N. Vekua. New methods for solving elliptic equations. John Wiley, North Holland, Amsterdam, 1967.
  • [70] G.M. Vörös and J. Jirousek. Application of the hybrid-Trefftz finite element model to thin shell analysis. In P. Ladeveze and O.C. Zienkiewicz, editors, Proc. European Conf. on New Advances in Comp. Struc. Mech., pages 547-554, Giens, France, 1991. Elsevier.
  • [71] A. Wroblewski and J. Jirousek. Application of hybrid-Trefftz p-elements to stress analysis in shafts. In Proc. XI Polish Conference on Comp. Meth. in Mech., volume 2, pages 983-990, Kielce-Cedzyna, Poland, 1993.
  • [72] A. Wroblewski, A.P. Zielinski, and J. Jirousek. Hybrid-Trefftz p-element for 3d axisymmetric problems of elasticity. In C. Hirsch, O. C. Zienkiewicz, and E. O nate, editors, Numerical Methods in Engineering '92, Proc. First Europ. Conf. on Numer. Meth. in Eng., pages 803-810, Brussels, 1992. Elsevier.
  • [73] A.P. Zielinski and I. Herrera. Trefftz method: fitting boundary conditions. International Journal for Numerical Methods in Engineering, 24:871-891, 1987.
  • [74] A.P. Zielinski and O.C. Zienkiewicz. Generalized finite element analysis with t-complete boundary solution functions. International Journal for Numerical Methods in Engineering, 21:509-528, 1985.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB1-0006-0047
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