# Iteratively solving a kind of signorini transmission problem in a unbounded domain

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 39, Issue: 4, page 715-726
- ISSN: 0764-583X

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topHu, Qiya, and Yu, Dehao. "Iteratively solving a kind of signorini transmission problem in a unbounded domain." ESAIM: Mathematical Modelling and Numerical Analysis 39.4 (2010): 715-726. <http://eudml.org/doc/194283>.

@article{Hu2010,

abstract = {
In this paper, we are concerned with a kind of Signorini
transmission problem in a unbounded domain. A variational
inequality is derived when discretizing this problem by coupled
FEM-BEM. To solve such variational inequality, an iterative
method, which can be viewed as a variant of the D-N alternative
method, will be introduced. In the iterative method, the finite
element part and the boundary element part can be solved
independently. It will be shown that the convergence speed of this
iteration is independent of the mesh size. Besides, a combination
between this method and the steepest descent method is also
discussed.
},

author = {Hu, Qiya, Yu, Dehao},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Signorini contact; FEM-BEM coupling; variational
inequality; D-N alternation; convergence rate.; variational inequality; convergence rate},

language = {eng},

month = {3},

number = {4},

pages = {715-726},

publisher = {EDP Sciences},

title = {Iteratively solving a kind of signorini transmission problem in a unbounded domain},

url = {http://eudml.org/doc/194283},

volume = {39},

year = {2010},

}

TY - JOUR

AU - Hu, Qiya

AU - Yu, Dehao

TI - Iteratively solving a kind of signorini transmission problem in a unbounded domain

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 39

IS - 4

SP - 715

EP - 726

AB -
In this paper, we are concerned with a kind of Signorini
transmission problem in a unbounded domain. A variational
inequality is derived when discretizing this problem by coupled
FEM-BEM. To solve such variational inequality, an iterative
method, which can be viewed as a variant of the D-N alternative
method, will be introduced. In the iterative method, the finite
element part and the boundary element part can be solved
independently. It will be shown that the convergence speed of this
iteration is independent of the mesh size. Besides, a combination
between this method and the steepest descent method is also
discussed.

LA - eng

KW - Signorini contact; FEM-BEM coupling; variational
inequality; D-N alternation; convergence rate.; variational inequality; convergence rate

UR - http://eudml.org/doc/194283

ER -

## References

top- C. Carstensen, Interface problem in holonomic elastoplasticity. Math. Methods Appl. Sci.16 (1993) 819–835. Zbl0792.73017
- C. Carstensen and J. Gwinner, FEM and BEM coupling for a nonlinear transmission problem with Signorini contact. SIAM J. Numer. Anal.34 (1997) 1845–1864. Zbl0896.65079
- C. Carstensen, M. Kuhn and U. Langer, Fast parallel solvers for symmetric boundary element domain decomposition equations. Numer. Math.79 (1998) 321–347. Zbl0907.65119
- M. Costabel and E. Stephan, Coupling of finite and boundary element methods for an elastoplastic interface problem. SIAM J. Numer. Anal.27 (1990) 1212–1226. Zbl0725.73090
- G. Gatica and G. Hsiao, On the coupled BEM and FEM for a nonlinear exterior Dirichlet problem in R2. Numer. Math.61(1992) 171–214. Zbl0741.65084
- R. Glowinski, Numerical methods for nonlinear variational problems. Springer-Verlag, New York (1984). Zbl0536.65054
- R. Glowinski, G. Golub, G. Meurant and J. Periaux, Eds., Proc. of the the First international symposium on domain decomposition methods for PDEs. SIAM Philadelphia (1988).
- Q. Hu and D. Yu, A solution method for a certain interface problem in unbounded domains. Computing67 (2001) 119–140. Zbl1109.65309
- N. Kikuchi and J. Oden, Contact problem in elasticity: a study of variational inequalities and finite element methods. SIAM, Philadelphia (1988). Zbl0685.73002
- J. Lions and E. Magenes, Non-homogeneous boundary value problems and applications, Vol. I. Springer-Verlag (1972). Zbl0223.35039
- P. Mund and E. Stephan, An adaptive two-level method for the coupling of nonlinear FEM-BEM equations, SIAM J. Numer. Anal.36 (1999) 1001–1021. Zbl0938.65138
- J. Necas, Introduction to the theory of nonlinear elliptic equations. Teubner, Texte 52, Leipzig (1983). Zbl0526.35003
- E. Polak, Computational methods in optimization. Academic Press, New York (1971).
- J. Schoberl, Solving the Signorini problem on the basis of domain decomposition techniques. Computing60 (1998) 323–344. Zbl0915.73077
- E. Stephan, W. Wendland and G. Hsiao, On the integral equation method for the plane mixed boundary value problem of the Laplacian. Math. Methods Appl. Sci.1 (1979) 265–321. Zbl0461.65082
- X. Tai and M. Espedal, Rate of convergence of some space decomposition methods for linear and nonlinear problems. SIAM J. Numer. Anal.35 (1998) 1558–1570. Zbl0915.65063
- X. Tai and J. Xu, Global convergence of space correction methods for convex optimization problems. Math. Comp.71 (2002) 105–122. Zbl0985.65065
- D. Yu, The relation between the Steklov-Poincare operator, the natural integral operator and Green functions. Chinese J. Numer. Math. Appl.17 (1995) 95–106.
- D. Yu, Discretization of non-overlapping domain decomposition method for unbounded domains and its convergence.Chinese J. Numer. Math. Appl.18 (1996) 93–102.
- D. Yu, Natural Boundary Integral Method and Its Applications. Science Press/Kluwer Academic Publishers, Beijing/New York (2002).

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