Incremental unknowns method and compact schemes

Jean-Paul Chehab

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

  • Volume: 32, Issue: 1, page 51-83
  • ISSN: 0764-583X

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Chehab, Jean-Paul. "Incremental unknowns method and compact schemes." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 32.1 (1998): 51-83. <http://eudml.org/doc/193867>.

@article{Chehab1998,
author = {Chehab, Jean-Paul},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {elliptic problems; nonlinear Galerkin method; compact scheme discretization; incremental unknowns method; preconditioning; numerical results; data compression method; Dirichlet problems},
language = {eng},
number = {1},
pages = {51-83},
publisher = {Dunod},
title = {Incremental unknowns method and compact schemes},
url = {http://eudml.org/doc/193867},
volume = {32},
year = {1998},
}

TY - JOUR
AU - Chehab, Jean-Paul
TI - Incremental unknowns method and compact schemes
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1998
PB - Dunod
VL - 32
IS - 1
SP - 51
EP - 83
LA - eng
KW - elliptic problems; nonlinear Galerkin method; compact scheme discretization; incremental unknowns method; preconditioning; numerical results; data compression method; Dirichlet problems
UR - http://eudml.org/doc/193867
ER -

References

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  1. [1] R. E. BANK, T. F. DUPONT, H. YSERENTANTThe Hierarchical Basis Multigrid Method, Numer. Math. 52, 1988, 4227-458. Zbl0645.65074MR932709
  2. [2] M. H. CARPENTER, D. GOTTLIEB, S. ABARBANEL, Time-Stable Boundary Conditions for Finite Difference Schemes Solving Hyperbolic Systems: Methodology and Application to High-Order Compact Schemes, J. comp. Phys. 111, 1994, 220-236. Zbl0832.65098MR1275021
  3. [3] J. P. CHEHAB, R. TEMAMIncremental Unknowns for Solving Nonlinear Eigenvalue Problems. New Multiresolution Methods, Numencal Methods for PDE's, 11, 199-228 (1995). Zbl0828.65124MR1325394
  4. [4] J. P. CHEHABA Nonlinear Adaptative Multiresolution Method in Finite Differences with Incremental Unknowns, M2AN, Vol. 29, 4, 451-475, 1995. Zbl0836.65114MR1346279
  5. [5] J. P. CHEHABSolution of Generalized Stokes Problems Using Hierarchical Methods and Incremental Unknowns, App. Num. Math., 21 (1996) 9-42. Zbl0853.76044MR1418694
  6. [6] M. CHEN, A. MIRANVILLE, R. TEMAMIncremental Unknows in Finite Differences in Space Dimension 3, Computational and Applied Mathematics, 14, 3, 1995, 1-15. MR1384185
  7. [7] M. CHEN, R. TEMAMIncremental Unknows for Solving Partial Differential Equations, Numesrische Mathematik, Springer Verlag, 59, 1991, 255-271. Zbl0712.65103MR1106383
  8. [8] M. CHEN, R. TEMAMIncremental Unknows in Finite Differences: Condition Number of the Matrix, SIAM. J. on Matrix Analysis and Applications (SIMAX), 14, n° 2, 1993, 432-455. Zbl0773.65080MR1211799
  9. [9] M. CHEN, R. TEMAMNonLinear Galerkin Method in Finite Difference case and Wavelet-like Incremental Unknowns, Numer. Math. 64, 1993, 271-294. Zbl0798.65093MR1206665
  10. [10] B. COCKBURN, C. W. SHUNonlinearly Stable Compact Schemes for shock calculations, ICASE Preprint series, May 1992. Zbl0805.65085MR1275104
  11. [11] L. COLLATZThe Numerical Treatment of Differential Equations, 3rd. ed., Springer Verlag, 1966. Zbl0086.32601MR109436
  12. [12] A. DEBUSSCHE, T. DUBOIS, R. TEMAMThe Nonlinear Galerkin Method: A Multiscale Method Applied to the Simulationof Homogeneous Turbulent Flows, Theorical and Computational Fluid Dynamics 7, 4, 1995, 279-315. Zbl0838.76060
  13. [13] S. K. LELECompact Finite Difference Schemes with Spectral like Resolution, J. Comp. Phys., 103, 16-42, 1992. Zbl0759.65006MR1188088
  14. [14] J. L. LIONS R. TEMAM, S. WANG, Splitting Up Methods and Numerical Analysis of Some Multiscale Problems, Computational Fluid Dynamics J, 5, 2, 1996, 279-315. 
  15. [15] M. MARION, R. TEMAMNonlinear Galerkin Methods, SIAM Journal of Numencal Analysis, 26, 1989, 1139-1157. Zbl0683.65083MR1014878
  16. [16] M. MARION, R. TEMAMNonlinear Galerkin Methods; The Finite Elements Case, Numensche Mathematik, 57, 1990, 205-226. Zbl0702.65081MR1057121
  17. [17] R. TEMAMInertial Manifolds and Multigrid Methods, SIAM. J. Math. Anal. 21, 1990, 154-178. Zbl0715.35039MR1032732
  18. [18] R. TEMAMInfinite Dimensional Dynamical Systems in Mechantes and Physics, Applied Mathematical Science, Springer Verlag, 68, 1988. Zbl0662.35001MR953967
  19. [19] H. A. VAN DER VORST. Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear System, SIAM. J. Sci. Stat. Comput., 13 (1992) 631-644. Zbl0761.65023MR1149111
  20. [20] H. YSERENTANT. On Multilevel Splitting of Finite Element Spaces, Numer. Math. 49, 1986, 379-412. Zbl0608.65065MR853662

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