1.
L. Andersson, N. Hall, B. Jawerth, and G. Peters, Wavelets on closed subsets of the real line, Topics in the Theory and Applications of Wavelets, Academic press, 1993, 1-14
2.
I. Babuska and A. Miller, A feedback finite element method with a-posteriori error estimation, I. The finite element method and some basic properties of the a posteriori error estimator, Comput. Methods Appl. Mech. Engrg. 61 (1987), 1-40
3.
I. Babuska and W. C. Rheinboldt, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal. 15 (1978), 736-754
4.
R. Balder and C. Zenger, The solution of multidimensional real Helmholtz equations on sparse grids, SIAM J. Sci. Comp. 17 (1996), 631-646
5.
R. E. Bank, T. F. Dupont, and H. Yserentant, The hierarchical basis multigrid method, Numer. Math. 52 (1988), 427-458
6.
R. E. Bank and A. Weiser, Some a posteriori error estimators for elliptic partial differential equations, Math. Comp. 44 (1985), 283-301
7.
A. Barinka, T. Barsch, P. Charton, A. Cohen, S. Dahlke, W. Dahmen, and U. Karsten, Adaptive wavelet schemes for elliptic problems - implementation and numerical experiments, SIAM J. Sci. Comput. 23 (2001), 910-939
8.
F. Bornemann, B. Erdmann, and R. Kornhuber, A posteriori error estimates for elliptic problems in two and three space dimensions, SIAM J. Numer. Anal. 33 (1996), 1188-1204
9.
A. Brandt, Multi-level adaptive solutions to boundary value problems, Math. Comput. 31 (1977), 333-390
10.
A. Brandt, Multi-level adaptive technique for fast numerical solution to boundary value problems, Proc. 3rd Int. Conf. on Numerical Methods in Fluid Mechanics, Lecture Notes in Physics, 18, 82-89, Springer-Verlag, 1973
11.
W. L. Briggs, A Multigrid Tutorial, SIAM, 1987
12.
H.-J. Bungatz, Dunne Gitter und deren Anwendung bei der adaptiven Losung der dreidimensionalen Poisson-Gleichung, Technischen Universitat Munchen, 1992
13.
M. A. Christon and D. W. Roach, The numerical performance of wavelets for PDEs: the multi-scale finite element, Comput. Mech. 25 (2000), 230-244
14.
A. Cohen, W. Dahmen, and R. DeVore, Adaptive wavelet methods for elliptic operator equations: Convergence rates, Math. Comp. 70 (2001), 27-75
15.
A. Cohen, I. Daubechies, and J.-C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math. 45 (1992), 485-560
16.
A. Cohen and R. Masson, Wavelet methods for second-order elliptic problems, preconditioning, and adaptivity, SIAM J. Sci. Comp. 21 (1999), 1006-1026
17.
S. Dahlke, W. Dahmen, R. Hochmuth, and R. Schneider, Stable multiscale bases and local error estimation for elliptic problems, Appl. Numer. Math. 23 (1997), 21-47
18.
W. Dahmen, Wavelet methods for PDEs - some recent developments, J. Comput. Appl. Math. 128 (2001), 133-185
19.
J. M. de Villiers, K. M. Goosen, and B. M. Herbst, Dubuc-Deslauriers subdivision for finite sequences and interpolation wavelets on an interval, SIAM J. Math. Anal. 35 (2003) 423452
20.
D. Donoho, Interpolating wavelet transform, Stanford University, 1992
21.
J. Douglas Jr., T. Dupont, and M. F. Wheeler, An $L^{\infty}$estimate and a super-convergence result for a Galerkin method for elliptic equations based on tensor products of piecewise polynomials, Rev. Francaise Automat. Informat. Recherche Operationnelle Ser Rouge 8 (1974), 61-66
22.
K. Eriksson, D. Estep, P. Hansbo, and C. Johnson, Introduction to adaptive methods for differential equations, Acta Numer. 4 (1995), 105-158
23.
D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, 1983
24.
M. Griebel, Adaptive sparse grid multilevel methods for elliptic PDEs based on finite diffrences, Computing 61 (1998), 151-179
25.
M. Griebel and S. Knapek, Optimized tensor-product approximation spaces, Constr. Approx. 16 (2000), 525-540
26.
W. Hackbusch, On the convergence of multigrid iterations, Beit. Numer. Math. 9 (1981), 231-329
27.
W. Hackbusch, On the multi-grid method applied to difference equations, Computing, 20 (1978), 291-306
28.
W. Hackbusch, Survey of convergence proofs for multigrid iterations, Special topics of applied mathematics, Proceedings, Bonn, Oct. 1979, 151-164, Elsevier, 1980
29.
G.-W. Jang, J. E. Kim, and Y. Y. Kim, Multiscale Galerkin method using inter- polation wavelets for two dimensional elliptic problems in general domains, Int. J. Numer. Methods Engrg. 59 (2004), 225-253
30.
Y. Y. Kim and G.-W. Jang, Hat interpolation wavelet-based multi-scale Galerkin method for thin-walled box beam analysis, Int. J. Numer. Methods Engrg. 53 (2002), 1575-1592
31.
P. Krysl, E. Grinspun and P. Schroder, Natural hierarchical refinement for finite element methods, Int. J. Numer. Methods Engrg. 56 (2003), 1109-1124
32.
S. Mallat, A wavelet tour of signal processing, Academic Press, 1998
33.
E. J. Stollnitz, T. D. DeRose, and D. H. Salesin, Wavelets for computer graphics: theory and applications, 21-31, Morgan Kaufmann publishers, 1996
34.
P. Wesseling, An introduction to multigrid methods, John Wiley & Sons, 1992
35.
H. Yserentant, On the multi-level splitting of finite element spaces, Numer. Math. 49 (1986), 379-412
36.
H. Yserentant, Two preconditioners based on the multi-level splitting of finite element spaces, Numer. Math. 58 (1990), 163-184
37.
C. Zenger, Sparse grids, Parallel algorithms for partial differential equations, Notes Numer. Fluid Mech., Vieweg 31 (1991)
38.
O. C. Zienkiewicz and A. Craig, Adaptive refinement, error estimates, multigrid solution, and hierarchic finite element method concepts, Accuracy Estimates and Adaptive Refinements in Finite Element Computations, 25-59, John Wiley & Sons, 1986
39.
O. C. Zienkiewicz, D. W. Kelly, J. Gago, and I. Babuska, Hierarchical finite element approaches, error estimates and adaptive refinement, The mathematics of finite elements and applications IV, 313 346, Academic Press, 1982
Journal title : Journal of the Korean Mathematical Society
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