A domain embedding method for Dirichlet problems in arbitrary space dimension

Andreas Rieder

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1998)

  • Volume: 32, Issue: 4, page 405-431
  • ISSN: 0764-583X

How to cite


Rieder, Andreas. "A domain embedding method for Dirichlet problems in arbitrary space dimension." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 32.4 (1998): 405-431. <http://eudml.org/doc/193880>.

author = {Rieder, Andreas},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {domain embedding method; Dirichlet problems; error estimates; preconditioning; numerical experiments},
language = {eng},
number = {4},
pages = {405-431},
publisher = {Dunod},
title = {A domain embedding method for Dirichlet problems in arbitrary space dimension},
url = {http://eudml.org/doc/193880},
volume = {32},
year = {1998},

AU - Rieder, Andreas
TI - A domain embedding method for Dirichlet problems in arbitrary space dimension
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1998
PB - Dunod
VL - 32
IS - 4
SP - 405
EP - 431
LA - eng
KW - domain embedding method; Dirichlet problems; error estimates; preconditioning; numerical experiments
UR - http://eudml.org/doc/193880
ER -


  1. [1] S. BERTOLUZZA, Interior estimates for the wavelet Galerkin method, Numer. Math. 78 (1997), pp. 1-20. Zbl0888.65113MR1483566
  2. [2] C. BORGERS and O. B. WIDLUND, On finite element domain imbedding methods, SIAM J. Numer. Anal., 27 (1990), pp. 963-978. Zbl0705.65078MR1051116
  3. [3] D. BRAESS, Finite-Elemente, Springer Lehrbuch, Springer-Verlag, Berlin, 1992. Zbl0754.65084
  4. [4] J. H. BRAMBLE and J. E. PASCIAK, New estimates for multilevel algorithms including the V-cycle, Math. Comp., 60 (1993), pp. 447-471. Zbl0783.65081MR1176705
  5. [5] J. H. BRAMBLE, J. E. PASCIAK and J. XU, Parallel multilevel preconditioners, Math. Comp., 55 (1990), pp. 1-22. Zbl0703.65076MR1023042
  6. [6] C. K. CHUI, Multivariate Splines, vol. 54 of CBMS-NSF Series in Applied Mathematics, SIAM, Philadelphia, 1988. Zbl0687.41018MR1033490
  7. [7] B. A. CIPRA, A rapid-deployment force for CFD : Cartesian grids, Siam News (Newsjournal of the Society for Industrial and Applied Mathematics), 25 (1995). 
  8. [8] A. COHEN, I. DAUBECHIES and J.-C. FEAUVEAU, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math., 45 (1992), pp. 485-560. Zbl0776.42020MR1162365
  9. [9] S. DAHLKE, V. LATOUR and K. GRÖCHENIG, Biorthogonal box spline wavelet bases, Bericht 122, Institut für Geometrie und Praktische Mathematik, RWTH Aachen, 1995. Zbl0946.65149
  10. [10] W. DAHMEN and A. KUNOTH, Multilevel preconditioning, Numer. Math., 63 (1992), pp. 315-344. Zbl0757.65031MR1186345
  11. [11] W. DAHMEN and C. A. MICCHELLI, Using the refinement equation for evaluating integrals of wavelets, SIAM J. Numer. Anal., 30 (1993), pp. 507-537. Zbl0773.65006MR1211402
  12. [12] W. DAHMEN, S. PRÖSSDORF and R. SCHNEIDER, Wavelet approximation methods for pseudodifferential equations I : Stability and convergence, Math. Z., 215 (1994), pp. 583-620. Zbl0794.65082MR1269492
  13. [13] I. DAUBECHIES, Orthonormal bases of compacity supported wavelets, Comm. Pure Appl. Math., 41 (1988), pp. 906-966. Zbl0644.42026MR951745
  14. [14] C. DE BOOR, K. HÖLLING and S. RIEMENSCHNEIDER, Box Splines, vol. 98 of Applied Mathematical Sciences, Springer-Verlag, Berlin, 1993. Zbl0814.41012MR1243635
  15. [15] P. DEUFLHARD and A. HOHMANN, Numerical Analysis : A First Course in Scientific Computation, de Gruyter Texbook, de Gruyter, Berlin, New York, 1994. Zbl0818.65002MR1325691
  16. [16] G. J. FIX and G. STRANG, A Fourier analysis of the finite element method in Ritz-Galerkin theory, in Constructive Aspects of Functional Analysis, Rome, 1973, Edizioni Cremonese, pp. 265-273. Zbl0179.22501MR258297
  17. [17] D. GILBARG and N. S. TRUDINGER, Elliptic Partial Differential Equations of Second Order, vol. 224 of Grundlehren der mathematischen Wissenshaften, Springer Verlag, Berlin, 1983. Zbl0562.35001MR737190
  18. [18] R. GLOWINSKI, Numerical Methods for Nonlinear Variational Problems, Springer Series in Computational Physics, Springer-Verlag, New York, 1984. Zbl0536.65054MR737005
  19. [19] R. GLOWINSKI and T.-W. PAN, Error estimates for fictitious domain/penalty/finite element methods, Calcolo, 19 (1992), pp. 125-141. Zbl0770.65066MR1219625
  20. [20] R. GLOWINSKI, T.-W. PAN, R. O. Jr. WELLS and X. ZHOU, Wavelet and finite element solutions for the Neumann problem using fictitious domains, J. Comp. Phys., 126 (1996), pp. 40-51. Zbl0852.65098MR1391621
  21. [21] R. GLOWINSKI, A. RIEDER, R. O. Jr. WELLS and X. ZHOU, A wavelet multilevel method for Dirichlet boundary value problems in general domains, Modélisation Mathématique et Analyse Numérique (M2AN), 30 (1996), pp. 711-729. Zbl0860.65121MR1419935
  22. [22] W. HACKBUSCH, Elliptic Differential Equations : Theory and Numerical Treatment, vol. 18 of Springer Series in Computational Mathematics, Springer Verlag, Heidelberg, 1992. Zbl0755.35021MR1197118
  23. [23] W. HACKBUSCH, Iterative Solution of Large Sparse Systems of Equations, Applied Mathematical Sciences, Springer-Verlag, New York, 1994. Zbl0789.65017MR1247457
  24. [24] R. H. W. HOPPE, Une méthode multigrille pour la solution des problèmes d'obstacle, Modélisation Mathématiques et Analyse Numérique (M2AN), 24 (1990), pp. 711-736. Zbl0716.65056MR1080716
  25. [25] S. JAFFARD, Wavelet methods for fast resolution of elliptic problems, SIAM J. Numer. Anal., 29 (1992), pp. 965-986. Zbl0761.65083MR1173180
  26. [26] A. KUNOTH, Computing refinable integrals documentation of the program, Manual Institut für Geometrie und Praktische Mathemtik, RWTH Aachen, 1995. 
  27. [27] Y. A. KUZNETSOV, S. A. FINOGENOV and A. V. SUPALOV, Fictitiuos domain methods for 3D elliptic problems: algorithms and software within a parallel environment, Arbeitspapiere der GMD 726, GMD, D-53754 St. Augustin, Germany, 1993. 
  28. [28] A. LATTO, H. L. RESNIKOFF and E. TENENBAUM, The evaluation of connection coefficients of compactly supported wavelets, in Proceedings of the USA-French Workshop on Wavelets and Turbulence, Princeton University, 1991. 
  29. [29] S. V. NEPOMNYASCHIKH, Mesh theorems of traces, normalization of function traces and their inversion, Sov. J. Numer. Anal. Math. Model., 6 (1991), pp. 223-242. Zbl0816.65097MR1126677
  30. [30] S. V. NEPOMNYASCHIKH, Fictitious space method on unstructured grids, East-West J. Numer. Math., 3 (1995), pp. 71-79. Zbl0831.65116MR1331485
  31. [31] J. A. NITSCHE, Ein Kriterium für die Quasi-Optimalität des Ritzschen Verfahrens, Numer. Math., 11 (1968), pp. 346-348. Zbl0175.45801MR233502
  32. [32] J. A. NITSCHE and A. H. SCHATZ, Interior estimates for Ritz-Galerkin methods, Math. Comp., 28 (1974), pp. 937-958. Zbl0298.65071MR373325
  33. [33] P. OSWALD, Multilevel Finite Element Approximation : Theory and Applications, Teubner Skripten zur Numerik, B. G. Teubner, Stuttgart, Germany, 1994. Zbl0830.65107MR1312165
  34. [34] G. STRANG and G. J. FIX, An Analysis of the Finite Element method, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Englewood Cliffs, N. J., 1973. Zbl0356.65096MR443377
  35. [35] R. O. Jr. WELLS and X. ZHOU, Wavelet-Galerkin solutions for the Dirichlet problem, Numer. Math., 70 (1995), pp. 379-396. Zbl0824.65108MR1330870
  36. [36] J. WLOKA, Partial Differential Equations, Cambridge University Press, Cambridge, U.K., 1987. Zbl0623.35006MR895589
  37. [37] J. XU, The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids, Computing, 56 (1996), pp. 215-235. Zbl0857.65129MR1393008

NotesEmbed ?


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.