Convergence of roundary element methods for numerical solutions of Fourier problems

Authors

  • Wojciech L. Golik University of Missouri at St. Louis.

DOI:

https://doi.org/10.22199/S07160917.1991.0017.00001

Keywords:

Method of contraction of the boundary, Volterra integral equations, Fundamental solutions, Heat equation

Abstract

Convergence proofs are given for the projection based boundary element methods for the numerical solution of various Fourier problems in regions with smooth compact boundaries. Volterra integral equations of the 2nd kind are formulated with associated integral operators mapping the space of continuous functions on a compactum into itself. The compactness of these operators ia shown, yielding the error estimates in supremum norme for a wide class of projection based BEMs. Extensions of the error analysis to the initial -boundary value problems of convective heat conduction are also discussed.

Author Biography

Wojciech L. Golik, University of Missouri at St. Louis.

Department pf Mathematics and Computer Science.

 

References

K.E. ATKINSON, A. Survey of Numerical Methods for the Solution of Fredholm Equations of the Second Type, SIAM, Philadelphia, 1976.

K.E. ATKINSON & F.R. DE HOOG, The numerical solution of Laplace's equation on a wedge, IMA J. Numer. Anal., v.4, 1984, p. 19.

C.T.H. BAKER, The Numerical Treatment of Numerical Equations, Oxford Univ. Press, London, 1977.

P.K. BANERJEE & R. BUTTERFIELD, Boundary Element Methods in Engineering Science, McGraw-Hill, London 1981.

C.A. BREBBIA, J.C.F. TELLES, & L.C. WROBEL, Boundary Element Techniques. Theory and Applications in Engineerinq, Springer-Verlag, Berlín, 1984.

G.A. CHANDLER, & I.G. GRAHAM, Product Integration- collocation methods for noncompact integral operator equations, Math. Comp., 50, 1988, pp. 125-138.

Y.P. CHANG, C.S. KANG, & D.J. CHEN, The use of fundamental Green functions for solutions of problems of heat conduction in anisotroric media, Int. J. Heat Mass Transfer, 16, 1973, pp. 1905-1918.

Published

2018-04-02

How to Cite

[1]
W. L. Golik, “Convergence of roundary element methods for numerical solutions of Fourier problems”, Proyecciones (Antofagasta, On line), vol. 10, no. 17, pp. 1-12, Apr. 2018.

Issue

Vol. 10 No. 17 (1991)

Section

Artículos
  • No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.