Adaptive coupling of boundary elements and finite elements
ESAIM: Modélisation mathématique et analyse numérique, Tome 29 (1995) no. 7, pp. 779-817.
@article{M2AN_1995__29_7_779_0,
     author = {Carstensen, Carsten and Stephan, Ernst P.},
     title = {Adaptive coupling of boundary elements and finite elements},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {779--817},
     publisher = {AFCET - Gauthier-Villars},
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     volume = {29},
     number = {7},
     year = {1995},
     mrnumber = {1364401},
     zbl = {0849.65083},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1995__29_7_779_0/}
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Carstensen, Carsten; Stephan, Ernst P. Adaptive coupling of boundary elements and finite elements. ESAIM: Modélisation mathématique et analyse numérique, Tome 29 (1995) no. 7, pp. 779-817. http://archive.numdam.org/item/M2AN_1995__29_7_779_0/

[1] I. Babuška, A. Miller, 1981, A posteriori error estimates and adaptive techniques for the finite element method, Univ. of Maryland, Institute for Physical Science and Technology, Tech. Note BN-968, College Park, MD.

[2] J. Bergh, J. Löfström, 1976, Interpolation spaces, Springer, Berlin. | MR | Zbl

[3] C. Carstensen, 1993, Interface problem in holonomie elastoplasticity, Math. Meth. in the Appl. Sc.16, 819-835. | MR | Zbl

[4] C. Carstensen, E. P. Stephan, 1996, Adaptive boundary element methods for some first kind integral equations, SIAM J. Numen Anal, (to appear). | MR | Zbl

[5] C. Carstensen, E. P. Stephan, 1993. Coupling of FEM and BEM for a Non-linear Interface Problem ; the h-p Version, Numerical Methods for Partial Differential Equations. (to appear). | MR | Zbl

[6] P. Clement, 1975, Approximation by finite element functions using local regularization, RAIRO, Ser. Rouge Anal Numer., R-2, pp. 77-84. | Numdam | MR | Zbl

[7] M. Costabel, 1987, Symmetrie methods for the coupling of finite elements and boundary elements, In : C. A. Brebia et al. (Eds.), Boundary Elements IX, Vol. 1,pp. 411-420, Springer-Verlag, Berlin.

[8] M. Costabel, 1988, Boundary integral operators on Lipschitz domains : Elementary results, SIAM J. Math. AnaL, 19, pp. 613-626. | Zbl

[9] M. Costabel, E. P. Stephan, 1985, A direct boundary integral equation method for transmission problems, J.Math. Anal. Appl., 106, pp. 367-413. | Zbl

[10] M. Costabel, E. P. Stephan, 1988, Coupling of finite and boundary elements for inhomogeneous transmission problems in R3, in Mathematics of Finite Elements and Applications VI, ed. J. R, Whiteman, pp.289-296, Academie Press. | Zbl

[11] M. Costabel, E. P. Stephan, 1990, Coupling of finite and boundary element methods for an elastoplastic interface problem, SIAM J. Nurnen Anal., 27, pp. 1212-1226. | Zbl

[12] D. A. Dunvant, 1995, High degree efficient symmetrical Gaussian quadrature rules for the triangle, Intern. J. Numer. Meth. Engin., 21, pp. 1129-1148. | Zbl

[13] K. Eriksson, C. Johnson, 1988, An adaptive finite element method for linear elliptic problems, Math. Comp., 50, pp, 361-383. | Zbl

[14] K. Eriksson, C. Johnson, 1991, Adaptive finite element methods for parabolicproblems. I. A linear model problem, SIAM J. Numer. Anal., 28, pp. 43-77. | Zbl

[15] V. Ervin, N. Heuer, E. P. Stephan, On the h-p version of the boundary element method for Symm's integral equation on polygons, To appear in Comput.Meth. Appl. Mech. Engin. | Zbl

[16] D. Gaier, 1976, Integralgleichungen erster Art und konforme Abbildung, Math.Z, 147, pp. 113-129. | Zbl

[17] G. N. Gatica, G. C. Hsiao, 1990, On a class of variational formulations for some nonlinear interface problems, Rendiconti di Mathematica Ser. VII, 10, pp. 681-715. | Zbl

[18] G. N. Gatica, G. C. Hsiao, 1992, On the coupled BEM and FEM for a nonlinear exterior Dirichlet problem in R2, Numer. Math., 61,pp, 171-214. | MR | Zbl

[19] H. Han, 1990, A new class of variational formulations for the coupling of finite and boundary element methods, J. Comput. Math., 8, pp. 223-232. | MR | Zbl

[20] C. Johnson, P. Hanseo, 1992, Adaptive finite element methods in computational mechanics. Comput Meth. Appl. Mech. Engin., 101, 143-181. | MR | Zbl

[21] J. L Lions, E. Magenes, 1972, Non-homogeneous boundary value problems and applications, Vol. I. Berlin-Heidelberg-New York : Springer. | MR | Zbl

[22] J. C. Nedelec, 1978, La méthode des éléments finis appliquée aux équations intégrales de la physique, First meeting AFCET-SMF on applied mathematics Palaiseau, Vol. 1, pp. 181-190. | Zbl

[23] F. V. Postell, E. P. Stephan, 1990, On the h-, p- and h-p versions of the boundary element method-numerical results, Computer Meth. in Appl. Mechanicsand Egin, 83, pp. 69-89. | MR | Zbl

[24] E. Rank, 1987, Adaptive boundary element methods in ; C. A. Brebbia, W. LWendland and G. Kuhn, eds., Boundary Elements, 9, Vol. 1, pp.259-273, Springer-Verlag, Heidelberg. | MR

[25] I. H Sloan, A. Spence, 1988, The Galerkin Method for Intégral Equations of thefirst kind with Logarithmic Kernel, Theory, IMA J. Numer. Anal, 8, pp. 105-122. | MR | Zbl

[26] E. P. Stephan, W. L. Wendland, 1984, An augmented Galerkin Procedure for the boundary integral method applied to two-dimensional screen and crack problems, Applicable Analysis, 18, pp. 183-219. | MR | Zbl

[27] H. H. Stroud, D. Secrest, 1966, Gaussian quadrature formulas, Prentice Hall,Englewood Cliff. | MR | Zbl

[28] R. Verfürth, 1992, A posteriori error estimates for non-linear problems. Finite element discretization of elliptic equations, Preprint. | MR

[29] W. L. Wendland, 1988, On Asymptotic Error Estimates for Combined BEM and FEM, in Finite and boundary element techniques from mathematical and engineering point of view, CISM Courses 301, E. Stein, W. L. Wendland, eds.,Springer-Verlag New York, pp. 273-331. | MR | Zbl

[30] W. L. Wendland, De-Hao Yu, 1988, Adaptive boundary element methods for strongly elliptic integral equations, Numer. Math., 53, pp. 539-558. | MR | Zbl

[31] W. L. Wendland, De-Hao Yu, 1992, A posteriori local error estimates ofboundary element methods with some pseudo-differential equations on closed curves, Journal for Computational Mathematics, 10, 273-289. | MR | Zbl

[32] E. Zeidler, 1990, Nonlinear functional analysis and its applications II, Vol. A and B, Springer-Verlag, New York. | MR | Zbl