Numerical Analysis of Partial Differential Equations

Numerical Analysis of Partial Differential Equations

Volumn , Issue , 2011, Pages 1-491

  Lui, S H ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; DISCRETE EVENT SIMULATION; DOMAIN DECOMPOSITION METHODS; LINEAR ALGEBRA; LINEAR SYSTEMS; NEWTON-RAPHSON METHOD; NUMERICAL METHODS;

DISCRETIZATION METHOD; ELLIPTIC PARTIAL DIFFERENTIAL EQUATION; MATHEMATICAL SCIENCE; MATHEMATICAL THEORY; NUMERICAL LINEAR ALGEBRA; SCIENCE AND ENGINEERING; SOLUTION OF LINEAR SYSTEMS; TIME DEPENDENT PDES;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 84949752532     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9781118111130     Document Type: Book

References (113)

1. R. A. Adams and J. J. F. Fournier. Soholev Spaces. Elsevier Science Ltd, Amsterdam, 2nd edition, 2003.
2. E. L. Allgower and K. Georg. Numerical Continuation Methods. Springer-Verlag, Berlin, 1990.
3. D. N. Arnold. A Concise Introduction to Numerical Analysis. http://www.ima.umn.edu/~arnold/597.00-01/nabook.pdf, 2001.
4. U. M. Ascher. Numerical Methods for Evolutionary differential equations. SIAM, Philadelphia, 2008.
5. H. Attouch, G. Buttazzo, and G. Michaille. Variational Analysis in Soholev and BV Spaces. SIAM, Philadelphia, 2006.
6. G. Aubert and P. Kornprobst. Mathematical Problems in Image Processing. Springer-Verlag, New York, 2nd edition, 2006.
7. O. Axelsson. Iterative Solution Methods. Cambridge University Press, New York, 1994.
8. O. Axelsson and V. A. Barker. Finite Element Solution of Boundary Value Problems. Academic Press, New York, 1984.
9. R. E. Bank. PLTMG: A Software Package for Solving Elliptic Partial Differential Equations:Users' Guide 8.0. SIAM, Philadelphia, 1998.
10. R. Beatson and L. Greengard. A short course on fast multipole methods. http://www.math.nyu.edu/faculty/greengar/shortcourse_fmm.pdf, 1996.
11. J.-D. Benamou, B. D. Froese, and A. M. Oberman. Finite difference schemes for the elliptic Monge-Ampere equation. M2AN, 44:737-758, 2010.
12. C. Bernardi and Y. Maday. Spectral methods. In P. G. Ciarlet and J. L. Lions, editors, Handbook of Numerical Analysis, volume 5, pages 209-485, North-Holland, Amsterdam, 1997.
13. L. Blum, F. Cucker, M. Shub, and S. Smale. Complexity and Real Computation. Springer-Verlag, New York, 1998.
14. J. P. Boyd. Chebyshev and Fourier Spectral Methods, 2nd Rev. Ed. Dover, Mineóla, New York, 2001.
15. D. Braess. Finite Elements. Cambridge University Press, Cambridge, 3rd edition, 2007.
16. J. H. Bramble and X. Zhang. The analysis of multigrid methods. In P. G. Ciarlet and J. L. Lions, editors, Handbook of Numerical Analysis, volume 7, North-Holland, Amsterdam, 2000.
17. S. Brenner and L. R. Scott. The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York, 3rd edition, 2008.
18. F. Brezzi and M. Fortin. Mixed and Hybrid Finite Element Methods. Springer-Verlag, Berlin, 1991.
19. W. L. Briggs, V. E. Henson, and S. F. McCormick. A Multigrid Tutorial. SIAM, Philadelphia, 2nd edition, 2000.
20. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang. Spectral Methods-Fundamentals in Single Domains. Springer-Verlag, New York, 2006.
21. C. Canuto, M. Y. Hussaini, A. Quarteroni, andT. A. Zang. Spectral Methods-Evolution to Complex Geometries and Applications to Fluid Dynamics. Springer-Verlag, New York, 2007.
22. R. H. F. Chan and X. Q. Jin. An Introduction to Iterative Toeplitz Solvers. SIAM, Philadelphia, 2007.
23. T.F. Chan and J. Shen. Image Processing and Analysis. SIAM, Philadelphia, 2005.
24. K. Chen. Matrix Preconditioning Techniques and Applications. Cambridge University Press, Cambridge, 2005.
25. Ph. G. Ciarlet. The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978.
26. Ph. G. Ciarlet. Mathematical Elasticity, Vol. I. North-Holland, Amsterdam, 1988.
27. D. Colton and R. Kress. Inverse Acoustic and Electromagnetic Scattering Theory. Springer-Verlag, Berlin, 2nd edition, 1998.
28. J. W. Demmel. Applied Numerical Linear Algebra. SIAM, 1997.
29. J. E. Dennis and R. B. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs, 1983.
30. M. O. Deville, P. F. Fischer, and E. H. Mund. High-Order Methods for Incompressible Fluid Flow. Cambridge University Press, Cambridge, 2002.
31. J. J. Dongarra, I. S. Duff, D. C. Sorensen, and H. van der Vorst. Numerical Linear Algebra on High-Performance Computers. SIAM, Philadelphia, 1998.
32. I. S. Duff, A. M. Erisman, and J. K. Reid. Direct Methods for Sparse Matrices. Oxford University Press, Oxford, 1986.
33. H. Elman, D. Silvester, and A. Wathen. Finite Elements and Fast Iterative Solvers. Oxford University Press, Oxford, 2005.
34. L. C. Evans. Partial Differential Equations. AMS, Providence, 1998.
35. C. Farhat and F. X. Roux. Implicit parallel processing in structural mechanics. Computational Mechanics Advances, 2:1-124, 1994.
36. A. S. Fokas. A Unified Approach to Boundary Value Problems. SIAM, Philadelphia, 2008.
37. G. B. Folland. Introduction to Partial Differential Equations. Princeton University Press, Princeton, N.J., 2nd edition, 1995.
38. B. Fornberg. A Practical Guide to Pseudospectral Methods. Cambridge University Press, Cambridge, 1996.
39. D. Funaro. Spectral Elements for Transport-Dominated Equations. Springer-Verlag, Berlin, 1997.
40. A. George and J. W. H. Liu. Computer Solution of Large Sparse Positive-Definite Systems. Prentice-Hall, New Jersey, 1981.
41. D. Gilbarg and N. S. Trudinger. Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin, 1983.
42. V. Girault and P. Raviart. Finite Element Methods for Navier-Stokes Equations. Springer, Berlin, 1986.
43. D. Givoli. Numerical Methods for Problems in Infinite Domains. Elsevier, Amsterdam, 1992.
44. R. Glowinski. Numerical methods for fluids. In P. G. Ciarlet and J. L. Lions, editors, Handbook of Numerical Analysis, volume 9, North-Holland, Amsterdam, 2003.
45. G. Golub and C. van Loan. Matrix Computations. John Hopkins U. P., Baltimore, 3rd edition, 1996.
46. D. Gottlieb and S. A. Orszag. Numerical Analysis of Spectral Methods. SIAM, Philadelphia, 1977.
47. M. Griebel, T. Dornseifer, and T. Neunhoeffer. Numerical Simulation in Fluid Dynamics. SIAM, Philadelphia, 1998.
48. P. Grisvard. Elliptic Problems in Nonsmooth Domains. Pitman, London, 1985.
49. C. Grossmann, H. G. Roos, and M. Stynes. Numerical Treatment of Partial Differential Equations. Springer-Verlag, Berlin, 2007.
50. J. L. Guermond, P. Minev, and J. Shen. An overview of projection methods for incompressible flows. Comput. Meth. Appl. Mech. Engrg, 195:6011-6045, 2006.
51. B. Y. Guo. Spectral Methods and Their Applications. World Scientific, Singapore, 1998.
52. B. Gustafsson, H. O. Kreiss, and J. Öliger. Time Dependent Problems and Difference Methods. John Wiley & Sons, Inc., New York, 1995.
53. W. Hackbusch. Multigrid Methods and Applications. Springer-Verlag, Berlin, 1985.
54. W. Hackbusch. Elliptic Differential Equations. Springer-Verlag, Berlin, 1992.
55. W. Hackbusch. Iterative Solution of Large Sparse Systems of Equations. Springer-Verlag, New York, 1994.
56. W. W. Hager and H. Zhang. A survey of nonlinear conjugate gradient methods. Pacific J. Optimization, 2:35-58, 2006.
57. T. Hagstrom. New results on absorbing layers and radiation boundary conditions. In M. Ainsworth et al., editor, Topics in Computational Wave Propagation, pages 1-42. Springer-Verlag, Berlin, 2003.
58. E. Hairer, C. Lubich, and G. Wanner. Geometric Numerical Integration. Springer-Verlag, Berlin, 2nd edition, 2006.
59. C. A. Hall and T. A. Porsching. Numerical Analysis of Partial Differential Equations. Prentice-Hall, Englewood Cliffs, N. J., 1990.
60. J. Hesthaven, S. Gottlieb, and D. Gottlieb. Spectral Methods for Time-Dependent Problems. Cambridge University Press, Philadelphia, 2007.
61. D. J. Higham and N. J. Higham. MATLAB Guide. SI AM, Philadelphia, 2nd edition, 2005.
62. N. J. Higham. Accuracy and Stability of Numerical Algorithms. SIAM, Philadelphia, 2nd edition, 2002.
63. A. Iserles. A fast and simple algorithm for the computation of Legendre coefficients. Numer. Math., 117:529-553, 2011.
64. J.M.Jin. The Finite Element Method if Electromagnetics. John Wiley & Sons, New York, 2nd edition, 2002.
65. C. Johnson. Numerical Solution of Partial Differential Equations by the Finite Element Method. Cambridge University Press, London, 1987.
66. H. Kardestuncer and D.H. Norrie, editors. Finite Element Handbook. McGraw-Hill, New York, 1987.
67. G. Kamiadakis and S. Sherwin. Spectrallhp Element Methods for Computational Fluid Dynamics. Oxford University Press, Oxford, 2nd edition, 2005.
68. H. B. Keller. Lectures on Numerical Methods in Bifurcation Problems. Springer-Verlag, Berlin, 1987.
69. C.T. Kelley. Iterative Methodsfor Linear and Nonlinear Equations. SIAM, Philadelphia, 1995.
70. P. Knabner and L. Angermann. Numerical Methods for Elliptic and Parabolic Partial Differential Equations. Springer-Verlag, New York, 2003.
71. H. O. Kreiss and J. Lorenz. Initial-Boundary Value Problems and the Navier-Stokes Equations. Academic Press, Inc., San Diego, 1989.
72. E. Kreyszig. Introductory Functional Analysis with Applications. John Wiley & Sons, New York, 1978.
73. M. C. Lai. A note on finite difference discretizations for Poisson equation on a disk. Numer. Meth.for PDEs, 17:199-203, 2001.
74. P. J. Lanzkron, D. J. Rose, and J. T. Wilkes. An analysis of approximate nonlinear elimination. SIAM J. Sei. Comput., 17:538-559, 1996.
75. J. L. Lions and E. Magenes. Nonhomogeneous Boundary Value Problems and Applications, volume I. Springer-Verlag, Berlin, 1972.
76. B. Lucquin and O. Pironneau. Introduction to Scientific Computing. John Wiley & Sons Ltd., Chichester, 1988.
77. G. I. Marchuk. Splitting and alternating direction method. In P. G. Ciarlet and J. L. Lions, editors, Handbook of Numerical Analysis, volume 1, pages 197-462, North-Holland, Amsterdam, 1990.
78. T. P. A. Mathew. Domain decomposition methods for the numerical solution of partial differential equations. In Lecture Notes in Computational Science and Engineering, volume 61, Springer-Verlag, Berlin, 2008.
79. S. F. McCormick, editor. Multigrid Methods. SI AM, Philadelphia, 1987.
80. J. A. Meijerink and H. A. van der Vorst. An iterative solution method for linear systems of which the coefficient matrix is a symmetric m-matrix. Math. Comp., 31:148-162, 1977.
81. K.W.Morton. Numerical Solution of Convection-Diffusion Problems. Chapman and Hall, London, 1996.
82. K. W. Morton and D. F. Mayers. Numerical Solution of Partial Differential Equations :An Introduction. Cambridge University Press, Cambridge, 2nd edition, 2005.
83. S. Osher and R. Fedkiw. Level Set Methods and Dynamic Implicit Suifaces. Springer-Verlag, 2003.
84. B. N. Parlett. The Symmetric Eigenvalue Problem. Prentice-Hall, Englewood Cliffs, 1980.
85. R. Peyret. Spectral Methods for Incompressible Viscous Flow. Springer-Verlag, New York, 2002.
86. E. Polak. Optimization: Algorithms and Consistent Approximations. Springer-Verlag, New York, 1997.
87. A. Quarteroni and A. Valli. Numerical Approximation of Partial Differential Equations. Springer-Verlag, Berlin, 1994.
88. A. Quarteroni and A. Valli. Domain Decomposition Methods for Partial Differential Equations. Oxford University Press, Oxford, 1999.
89. B. D. Reddy. Introductory Functional Analysis. Springer-Verlag, New York, 1998.
90. M. Renardy and R. C. Rogers. An Introduction to Partial Differential Equations. Springer-Verlag, New York, 2nd edition, 2004.
91. R. D. Richtmyer and K. W. Morton. Difference Methods for Initial Value Problems. John Wiley and Sons, Inc., London, 2nd edition, 1967.
92. H-G Roos, M. Stynes, and L. Tobiska. Robust Numerical Methods for Singularly Perturbed Differential Equations. Springer-Verlag, Berlin, 2nd edition, 2008.
93. Y. Saad. Iterative Methods for Sparse Linear Systems. SI AM, Philadelphia, 2nd edition, 2003.
94. Ch. Schwab, p- and hp- Finite Element Methods. Oxford University Press, Oxford, 1998.
95. J. Sethian. Level Set Methods. Cambridge University Press, 2nd edition, 2000.
96. J. Shen and T. Tang. Spectral and High-Order Methods with Applications. Science Press, Beijing, 2006.
97. B. F. Smith, P. Bjorstad, and W. D. Gropp. Domain Decomposition : Parallel Multilevel Algorithms for Elliptic Partial Differential Equations. Cambridge University Press, New York, 1996.
98. G. Strang and G. J. Fix. An Analysis of the Finite Element Method. Prentice-Hall, Englewood Cliffs, N. J., 1973.
99. J. C. Strikwerda. Finite Difference Schemes and Partial Differential Equations. SIAM, Philadelphia, 2nd edition, 2004.
100. A. Taflove and S. C. Hagness. Computational Electrodynamics: The Finite-Difference Time-Domain Method. Artech House Publishers, Boston, 3rd edition, 2005.
101. P. Le Tallec. Domain decomposition methods in computational mechanics. Computational Mechanics Advances, 1:121-220, 1994.
102. R. Temam. Navier-Stokes Equations. North-Holland, Amsterdam, 1984.
103. V. Thomee. Galerkin Finite Element Methods for Parabolic Problems. Springer-Verlag, Berlin, 1997.
104. J. Thompson, B. Soni, and N. P. Wheatherill. Handbook of Grid Generation. CRC Press, Boca Raton, 1999.
105. A. Toselli and O. Widlund. Domain Decomposition Methods-Algorithms and Theory. Springer-Verlag, Berlin, 2005.
106. L. N. Trefethen. Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/pdetext.html, 1996.
107. L. N. Trefethen. Spectral Methods in Matlab. SIAM, Philadelphia, 2000.
108. L. N. Trefethen and M. Embree. Spectra and Pseudospectra. Princeton University Press, Princeton, 2005.
109. L. N. Trefethen and D. Bau HI. Numerical Linear Algebra. SIAM, Philadelphia, 1997.
110. U. Trottenberg, C. Oosterlee, and A. Schuller. Multigrid. Academic Press, London, 2001.
111. J. Xu. Iterative methods by space decomposition and subspace correction. SIAM Rev., 34:581-613, 1992.
112. J. Xu and J. Zou. Some nonoverlapping domain decomposition methods. SIAM Rev., 40:857-914, 1998.
113. D. Yu. Natural Boundary Integral Method and its Applications. Science Press, Beijing, 2002.