Adaptive coupling of boundary elements and finite elements

Carsten Carstensen; Ernst P. Stephan

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1995)

  • Volume: 29, Issue: 7, page 779-817
  • ISSN: 0764-583X

How to cite

top

Carstensen, Carsten, and Stephan, Ernst P.. "Adaptive coupling of boundary elements and finite elements." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 29.7 (1995): 779-817. <http://eudml.org/doc/193792>.

@article{Carstensen1995,
author = {Carstensen, Carsten, Stephan, Ernst P.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {boundary element method; finite element method; symmetric coupling; adaptivity; boundary integral operators; Galerkin discretization; Cea-type discretization error estimates; numerical test examples},
language = {eng},
number = {7},
pages = {779-817},
publisher = {Dunod},
title = {Adaptive coupling of boundary elements and finite elements},
url = {http://eudml.org/doc/193792},
volume = {29},
year = {1995},
}

TY - JOUR
AU - Carstensen, Carsten
AU - Stephan, Ernst P.
TI - Adaptive coupling of boundary elements and finite elements
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1995
PB - Dunod
VL - 29
IS - 7
SP - 779
EP - 817
LA - eng
KW - boundary element method; finite element method; symmetric coupling; adaptivity; boundary integral operators; Galerkin discretization; Cea-type discretization error estimates; numerical test examples
UR - http://eudml.org/doc/193792
ER -

References

top
  1. [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. [2] J. BERGH, J. LÖFSTRÖM, 1976, Interpolation spaces, Springer, Berlin. Zbl0344.46071MR482275
  3. [3] C. CARSTENSEN, 1993, Interface problem in holonomie elastoplasticity, Math. Meth. in the Appl. Sc.16, 819-835. Zbl0792.73017MR1245631
  4. [4] C. CARSTENSEN, E. P. STEPHAN, 1996, Adaptive boundary element methods for some first kind integral equations, SIAM J. Numen Anal, (to appear). Zbl0863.65073MR1427458
  5. [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). Zbl0833.65123MR1345759
  6. [6] P. CLEMENT, 1975, Approximation by finite element functions using local regularization, RAIRO, Ser. Rouge Anal Numer., R-2, pp. 77-84. Zbl0368.65008MR400739
  7. [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. [8] M. COSTABEL, 1988, Boundary integral operators on Lipschitz domains : Elementary results, SIAM J. Math. AnaL, 19, pp. 613-626. Zbl0644.35037
  9. [9] M. COSTABEL, E. P. STEPHAN, 1985, A direct boundary integral equation method for transmission problems, J.Math. Anal. Appl., 106, pp. 367-413. Zbl0597.35021
  10. [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. Zbl0687.73034
  11. [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. Zbl0725.73090
  12. [12] D. A. DUNVANT, 1995, High degree efficient symmetrical Gaussian quadrature rules for the triangle, Intern. J. Numer. Meth. Engin., 21, pp. 1129-1148. Zbl0589.65021
  13. [13] K. ERIKSSON, C. JOHNSON, 1988, An adaptive finite element method for linear elliptic problems, Math. Comp., 50, pp, 361-383. Zbl0644.65080
  14. [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. Zbl0732.65093
  15. [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. Zbl0842.65076
  16. [16] D. GAIER, 1976, Integralgleichungen erster Art und konforme Abbildung, Math.Z, 147, pp. 113-129. Zbl0304.30006
  17. [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. Zbl0767.35019
  18. [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. Zbl0741.65084MR1147576
  19. [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. Zbl0712.65093MR1299224
  20. [20] C. JOHNSON, P. HANSEO, 1992, Adaptive finite element methods in computational mechanics. Comput Meth. Appl. Mech. Engin., 101, 143-181. Zbl0778.73071MR1195583
  21. [21] J. L LIONS, E. MAGENES, 1972, Non-homogeneous boundary value problems and applications, Vol. I. Berlin-Heidelberg-New York : Springer. Zbl0223.35039MR350177
  22. [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. Zbl0486.45008
  23. [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. Zbl0732.65101MR1078696
  24. [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. MR965323
  25. [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. Zbl0636.65143MR967846
  26. [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. Zbl0522.73083MR767500
  27. [27] H. H. STROUD, D. SECREST, 1966, Gaussian quadrature formulas, Prentice Hall,Englewood Cliff. Zbl0156.17002MR202312
  28. [28] R. VERFÜRTH, 1992, A posteriori error estimates for non-linear problems. Finite element discretization of elliptic equations, Preprint. MR1213837
  29. [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. Zbl0672.65089MR1002581
  30. [30] W. L. WENDLAND, DE-HAO YU, 1988, Adaptive boundary element methods for strongly elliptic integral equations, Numer. Math., 53, pp. 539-558. Zbl0657.65138MR954769
  31. [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. Zbl0758.65072MR1167929
  32. [32] E. ZEIDLER, 1990, Nonlinear functional analysis and its applications II, Vol. A and B, Springer-Verlag, New York. Zbl0684.47029MR816732

Citations in EuDML Documents

top
  1. Markus Aurada, Michael Feischl, Dirk Praetorius, Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems
  2. Markus Aurada, Michael Feischl, Dirk Praetorius, Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems
  3. Mauricio A. Barrientos, Gabriel N. Gatica, Matthias Maischak, 𝐴 - 𝑃𝑂𝑆𝑇𝐸𝑅𝐼𝑂𝑅𝐼 error estimates for linear exterior problems 𝑉𝐼𝐴 mixed-FEM and DtN mappings
  4. Mauricio A. Barrientos, Gabriel N. Gatica, Matthias Maischak, error estimates for linear exterior problems mixed-FEM and DtN mappings

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.