A domain embedding method for Dirichlet problems in arbitrary space dimension
- Volume: 32, Issue: 4, page 405-431
- ISSN: 0764-583X
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topRieder, 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>.
@article{Rieder1998,
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},
}
TY - JOUR
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 -
References
top- [1] S. BERTOLUZZA, Interior estimates for the wavelet Galerkin method, Numer. Math. 78 (1997), pp. 1-20. Zbl0888.65113MR1483566
- [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] D. BRAESS, Finite-Elemente, Springer Lehrbuch, Springer-Verlag, Berlin, 1992. Zbl0754.65084
- [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] J. H. BRAMBLE, J. E. PASCIAK and J. XU, Parallel multilevel preconditioners, Math. Comp., 55 (1990), pp. 1-22. Zbl0703.65076MR1023042
- [6] C. K. CHUI, Multivariate Splines, vol. 54 of CBMS-NSF Series in Applied Mathematics, SIAM, Philadelphia, 1988. Zbl0687.41018MR1033490
- [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] 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] 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] W. DAHMEN and A. KUNOTH, Multilevel preconditioning, Numer. Math., 63 (1992), pp. 315-344. Zbl0757.65031MR1186345
- [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] 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] I. DAUBECHIES, Orthonormal bases of compacity supported wavelets, Comm. Pure Appl. Math., 41 (1988), pp. 906-966. Zbl0644.42026MR951745
- [14] C. DE BOOR, K. HÖLLING and S. RIEMENSCHNEIDER, Box Splines, vol. 98 of Applied Mathematical Sciences, Springer-Verlag, Berlin, 1993. Zbl0814.41012MR1243635
- [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] 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] 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] R. GLOWINSKI, Numerical Methods for Nonlinear Variational Problems, Springer Series in Computational Physics, Springer-Verlag, New York, 1984. Zbl0536.65054MR737005
- [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] 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] 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] W. HACKBUSCH, Elliptic Differential Equations : Theory and Numerical Treatment, vol. 18 of Springer Series in Computational Mathematics, Springer Verlag, Heidelberg, 1992. Zbl0755.35021MR1197118
- [23] W. HACKBUSCH, Iterative Solution of Large Sparse Systems of Equations, Applied Mathematical Sciences, Springer-Verlag, New York, 1994. Zbl0789.65017MR1247457
- [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] S. JAFFARD, Wavelet methods for fast resolution of elliptic problems, SIAM J. Numer. Anal., 29 (1992), pp. 965-986. Zbl0761.65083MR1173180
- [26] A. KUNOTH, Computing refinable integrals documentation of the program, Manual Institut für Geometrie und Praktische Mathemtik, RWTH Aachen, 1995.
- [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] 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] 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] S. V. NEPOMNYASCHIKH, Fictitious space method on unstructured grids, East-West J. Numer. Math., 3 (1995), pp. 71-79. Zbl0831.65116MR1331485
- [31] J. A. NITSCHE, Ein Kriterium für die Quasi-Optimalität des Ritzschen Verfahrens, Numer. Math., 11 (1968), pp. 346-348. Zbl0175.45801MR233502
- [32] J. A. NITSCHE and A. H. SCHATZ, Interior estimates for Ritz-Galerkin methods, Math. Comp., 28 (1974), pp. 937-958. Zbl0298.65071MR373325
- [33] P. OSWALD, Multilevel Finite Element Approximation : Theory and Applications, Teubner Skripten zur Numerik, B. G. Teubner, Stuttgart, Germany, 1994. Zbl0830.65107MR1312165
- [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] R. O. Jr. WELLS and X. ZHOU, Wavelet-Galerkin solutions for the Dirichlet problem, Numer. Math., 70 (1995), pp. 379-396. Zbl0824.65108MR1330870
- [36] J. WLOKA, Partial Differential Equations, Cambridge University Press, Cambridge, U.K., 1987. Zbl0623.35006MR895589
- [37] J. XU, The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids, Computing, 56 (1996), pp. 215-235. Zbl0857.65129MR1393008
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