Hu, Qiya; Yu, Dehao A coupling of FEM-BEM for a kind of Signorini contact problem. (English) Zbl 0995.49010 Sci. China, Ser. A 44, No. 7, 895-906 (2001). Summary: We consider a kind of coupled nonlinear problem with Signorini contact conditions. To solve this problem, we discuss a new coupling of finite element and boundary element by adding an auxiliary circle. We first derive an asymptotic error estimate of the approximation to the coupled FEM-BEM variational inequality. Then we design an iterative method for solving the coupled system, in which only three standard subproblems without involving any boundary integral equation are solved. It is shown that the convergence speed of this iteration method is independent of the mesh size. MSC: 49J40 Variational inequalities 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 74M15 Contact in solid mechanics 65N38 Boundary element methods for boundary value problems involving PDEs 35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000) Keywords:FEM-BEM coupling; convergence rate; Signorini contact; finite element; boundary element; variational inequality; iteration method PDFBibTeX XMLCite \textit{Q. Hu} and \textit{D. Yu}, Sci. China, Ser. A 44, No. 7, 895--906 (2001; Zbl 0995.49010) Full Text: DOI References: [1] Carstensen, C.; Gwinner, J., FEM and BEM coupling for a nonlinear transmission problem with Signorini contact, SIAM J. Numer. Anal., 34, 6, 1845-1864 (1997) · Zbl 0896.65079 [2] Costabel, M.; Stephan, E., Coupling of finite and boundary element methods for an elastoplastic interface problem, SIAM J. Numer. Anal., 27, 4, 1212-1226 (1990) · Zbl 0725.73090 [3] Kikuchi, N.; Oden, J., Contact problem in elasticity : a study of variational inequalities and finite element methods (1988), Philadelphia: SIAM, Philadelphia · Zbl 0685.73002 [4] Necas, J., Introduction to the Theory of Nonlinear Elliptic Equations (1983), Leipzig: Teubner, Leipzig · Zbl 0526.35003 [5] Carstensen, C., Interface problem in holonomic elastoplasticity, Math. Methods Appl. Sci., 16, 11, 819-835 (1993) · Zbl 0792.73017 [6] Gatica, G.; Hsiao, G., On the coupled BEM and FEM or a nonlinear exterior Dirichlet problem in ℝ, Numer. Math., 61, 2, 171-214 (1992) · Zbl 0741.65084 [7] Mund, P.; Stephan, E., An adaptive two-level method for the coupling of nonlinear FEM-BEM equations, SIAM J. Numer. Anal., 36, 3, 1001-1021 (1999) · Zbl 0938.65138 [8] Meddahi, S., An optimal iterative process for the Johnson- Nedelec method of coupling boundary and finite elements, SIAM J. Numer. Anal., 35, 4, 1393-1415 (1998) · Zbl 0912.65096 [9] Yu, D., The Mathematical Theory of the Natural Boundary Element Methods (in Chinese) (1993), Beijing: Science Press, Beijing [10] Lions, J.; Magenes, E., Non-homogeneous Boundary Value Problems and Applications (1972), Berlin-Heidelberg-New York: Springer-Verlag, Berlin-Heidelberg-New York · Zbl 0227.35001 [11] Zenisek, A., Nonlinear Elliptic and Evolution Problems and Their Finite Element Approximations (1990), London: Academic Press, London · Zbl 0731.65090 [12] Costabel, M., Boundary integral operators on Lipschitz domains : Elementary results, SIAM J. Numer. Math. Anal., 19, 2, 613-626 (1988) · Zbl 0644.35037 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.