Abstract
A boundary method for solving the biharmonic equation is presented. It is based on the use of systems of solutions of the homogeneous equations, which are complete. A convenient criterium for the completeness of such systems, is the notion of c-completeness. Using a convenient representation of solutions for the biharmonic equation a procedure for constructing c-complete systems for this equation is developed. Examples of such systems are constructed.
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References
Bates, R.H.T. (1975) Analytic Constraints on Electro-magnetic Field Computations. IEEE Trans. on Microwave Theory of Techniques. 23, 605–623.
Brebbia, C.A. (1978) The Boundary Element Method for Engineers. Pentech Press. London.
Glowinski, R., and Pironneau, O. (1978) On Numerical Methods for the Stokes Problem. Chapter 13 of Energy Methods in Finite Element Analysis. R. Glowinski, E.Y. Rodin and O.C. Zienkiewicz, ed., Wiley and Sons.
Herrera, I. (1977a) General Variational Principles Applicable to the Hybrid Element Method. Proc. Nat. Acad. Sci. USA, 74, 7:2595–2597.
Herrera, I. (1979a) On the Variational Principles of Mechanics. Trends in Applications of Pure Mathematics to Mechanics. II, 115-128, H. Zorsky, ed., Pitman Publishing Limited (Invited general lecture)
Herrera, I. (1979b) Theory of Connectivity: A Systematic Formulation of Boundary Element Methods. Applied Mathematical Modelling. 3, 2:151–156.
Herrera, I. (1980b) Variational Principles for Problems with Linear Constraints. Prescribed Jumps and Continuation Type Restrictions. Jour. Inst. Maths. Applics. 25, 67–96.
Herrera, I. (1980c) Boundary Methods in Flow Problems. Proc. Third International Conference on Finite Elements in Flow Problems, Banff, Canada, 10–13 June, 30-42. (Invited general lecture).
Herrera, I. (1980d) Boundary Methods in Water Resources. Finite Elements in Water Resources, S.Y. Wang, et al., ed., The University of Mississippi, 58-71. (Invited general lecture).
Herrera, I. (1980e) Boundary Methods. A Criterion for Completeness. Proc. Nat. Acad. Sci. USA, 77, 8:4395–4398.
Herrera, I. (1981a) An Algebraic Theory of Boundary Value Problems. Comunicaciones Técnicas, IIMAS-UNAM. (In press).
Herrera, I. (1981b) Boundary Methods in Fluids. Finite Elements in Fluids, Volume IV, R.H. Gallagher, ed., John Wiley and Sons. (In press).
Herrera, I. (1981c) Boundary Methods. Theoretical Foundations for Numerical Applications of Complete Systems of Solutions. Comunicaciones Técnicas, IIMAS-UNAM.
Herrera, I., and Sabina, F.J. (1978) Connectivity as an Alternative to Boundary Integral Equations. Construction of bases. Proc. Nat. Acad. Sci. USA, 75, 5:2059–2063.
Kupradze, V.D. (1967) On the Approximate Solution of Problems in Mathematical Physics. Russian Math. Surveys. 22, 2:58–108. (Uspehi Mat. Nauk. 22, 2:59-107).
Lions, J.L., and Magenes, E. (1972) Non-homogeneous Boundary Value Problems and Applications. Springer-Verlag, New York.
Millar, R.F. (1973) The Rayleigh Hypothesis and a Related Least-Squares Solutions to Scattering Problems for Periodic Surfaces and other Scatterers. Radio Science. 8, 785–796.
Miranda, C. (1970) Partial Differential Equations of Elliptic Type. 2nd Ed., Springer-Verlag, New York. (Translation of Equazioni alle Derivate Parziali di Tipo Ellitico, 1955).
Sánchez-Sesma, F.J., Herrera, I., and Avilés, J. (1981) Boundary Methods for Elastic Wave Diffraction-Application to Scattering of SH Waves by Surface Irregularities. Comunicaciones Técnicas, IIMAS-UNAM. (In press).
Temam, R. (1977) Navier Stokes Equations: Theory and Numerical Analysis. North-Holland, Amsterdam.
Trefftz, E. (1926) Ein Gegenstruck zum Ritzschen Vergaren. Proc. 2nd. Int. Congress Appl. Mech. Zurich.
Zienkiewicz, O.C. (1977) The Finite Element Method in Engineering Science. Mc-Graw Hill, New York.
Zienkiewicz, O.C., Kelly, D.W., and Bettess P., (1977) The Coupling of the Finite Element Methods and Boundary Solution Procedures. Int. J. Num. Math. Eng. 11, 355–377.
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Gourgeon, H., Herrera, I. (1981). Boundary Methods. C-Complete Systems for the Biharmonic Equations. In: Brebbia, C.A. (eds) Boundary Element Methods. Boundary Elements, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11270-0_27
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DOI: https://doi.org/10.1007/978-3-662-11270-0_27
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