Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


A direct boundary element method for Signorini problems
HTML articles powered by AMS MathViewer

by Hou De Han PDF
Math. Comp. 55 (1990), 115-128 Request permission


In this paper, a Signorini problem is reduced to a variational inequality on the boundary, and a direct boundary element method is presented for its solution. Furthermore, error estimates for the approximate solutions of Signorini problems are given. In addition, we show that the Signorini problem may be formulated as a saddle-point problem on the boundary.
  • J. M. Aitchison, A. A. Lacey, and M. Shillor, A model for an electropaint process, IMA J. Appl. Math. 33 (1984), no. 1, 17–31. MR 763400, DOI 10.1093/imamat/33.1.17
  • Ivo Babuška and A. K. Aziz, Survey lectures on the mathematical foundations of the finite element method, The mathematical foundations of the finite element method with applications to partial differential equations (Proc. Sympos., Univ. Maryland, Baltimore, Md., 1972) Academic Press, New York, 1972, pp. 1–359. With the collaboration of G. Fix and R. B. Kellogg. MR 0421106
  • Haïm Brézis, Problèmes unilatéraux, J. Math. Pures Appl. (9) 51 (1972), 1–168. MR 428137
  • G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique, Travaux et Recherches Mathématiques, No. 21, Dunod, Paris, 1972 (French). MR 0464857
  • Gaetano Fichera, Problemi elastostatici con vincoli unilaterali: Il problema di Signorini con ambigue condizioni al contorno, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia (8) 7 (1963/64), 91–140 (Italian). MR 178631
  • Avner Friedman, Variational principles and free-boundary problems, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1982. MR 679313
  • Roland Glowinski, Numerical methods for nonlinear variational problems, Springer Series in Computational Physics, Springer-Verlag, New York, 1984. MR 737005, DOI 10.1007/978-3-662-12613-4
  • Roland Glowinski, Jacques-Louis Lions, and Raymond Trémolières, Numerical analysis of variational inequalities, Studies in Mathematics and its Applications, vol. 8, North-Holland Publishing Co., Amsterdam-New York, 1981. Translated from the French. MR 635927
  • Hou De Han, The boundary finite element methods for Signorini problems, Numerical methods for partial differential equations (Shanghai, 1987) Lecture Notes in Math., vol. 1297, Springer, Berlin, 1987, pp. 38–49. MR 929036, DOI 10.1007/BFb0078538
  • Hou De Han, Boundary integro-differential equations of elliptic boundary value problems and their numerical solutions, Sci. Sinica Ser. A 31 (1988), no. 10, 1153–1165. MR 976775
  • —, A new class of variational formulations for the coupling of finite and boundary element methods (to appear).
  • George C. Hsiao and Wolfgang L. Wendland, A finite element method for some integral equations of the first kind, J. Math. Anal. Appl. 58 (1977), no. 3, 449–481. MR 461963, DOI 10.1016/0022-247X(77)90186-X
  • M. N. Le Roux, Méthode d’éléments finis pour la résolution numérique de problèmes extérieurs en dimension $2$, RAIRO Anal. Numér. 11 (1977), no. 1, 27–60, 112 (French, with English summary). MR 448954, DOI 10.1051/m2an/1977110100271
  • J.-L. Lions, Optimal control of systems governed by partial differential equations. , Die Grundlehren der mathematischen Wissenschaften, Band 170, Springer-Verlag, New York-Berlin, 1971. Translated from the French by S. K. Mitter. MR 0271512
  • J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications. I, Springer-Verlag, Berlin, 1972.
  • J.-C. Nédélec, Integral equations with nonintegrable kernels, Integral Equations Operator Theory 5 (1982), no. 4, 562–572. MR 665149, DOI 10.1007/BF01694054
  • A. Signorini, Sopra alcune questioni di elastostatica, Atti della Società Italiana per il Progresso della Scienza, 1933.
Similar Articles
Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 55 (1990), 115-128
  • MSC: Primary 65N30; Secondary 49J40, 65K05
  • DOI:
  • MathSciNet review: 1023048