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Mathematics of Computation
Journal of the American Mathematical Society
ISSN 1088-6842(e) ISSN 0025-5718(p)
     

REVIEWS AND DESCRIPTIONS OF TABLES AND BOOKS

Book reviews do not contain an abstract. You may download the entire set of reviews from this issue using the links below.

Review information:

Journal: Math. Comp. 74, 1033-1052
DOI:

PII:
S 0025-5718(04)01757-0
Posted: November 22, 2004
Copyright of article: Copyright 2004, American Mathematical Society
Retrieve reviews in: PDF

Report on global methods for combinatorial isoperimetric problems, by L. H. Harper
Cambridge Studies in Advanced Mathematics, vol. 90, Cambridge University Press, 2004, xiv+231, hardcover, $60.00
2000 Mathematics Subject Classification. Primary 05C35, 90C27, 52B60

Reviewed by: Igor Shparlinski
E-mail address: igor@comp.mq.edu.au



Adaptive finite element methods for differential equations, by Wolfgang Bangerth and Rolf Rannacher
Lectures in Mathematics ETH Z\"{u}rich, Birkhäuser Verlag, Basel, 2003, viii+207, softcover, EUR 22.00/SF 35.00
2000 Mathematics Subject Classification. Primary 65L60, 65L70, 65M60, 65Nxx, 74S05, 76M10

Reviewed by: Endre Suli
Affiliation: University of Oxford

References:

1.
M. Ainsworth and J.T. Oden. A posteriori Error Estimation in Finite Element Analysis. Wiley, New York, 2000.

2.
I. Babuska and W.C. Rheinboldt. Error estimates for adaptive finite element computations. SIAM J. Numer. Anal., 15:736-754, 1978.

3.
I. Babuska and W.C. Rheinboldt. A posteriori error estimation for the finite element method. Int. J. Numer. Meth. Eng., 12:1597-1615, 1978.

4.
I. Babuska and T. Strouboulis. The Finite Element Method and Its Reliability. Oxford University Press, Oxford, 2001.

5.
C. Carstensen. Estimation of higher Sobolev norm from lower order approximation. SIAM J. Numer. Anal. (Accepted for publication, 2004).

6.
R. Courant. Variational methods for the solution of problems of equilibrium and vibration. Bull. Amer. Math. Soc., 49, 1-23, 1943.

7.
R. Becker and R. Rannacher. Weighted a posteriori error control in FE methods. Lecture at ENUMATH-95, Paris, Sept. 18-22, 1995, Preprint 96-01, SFB 359, University of Heidelberg, PROC. ENUMATH'97 (H.G. Brock et al., eds.), pp.621-637, World Scientific, Singapore, 1998.

8.
R. Becker and R. Rannacher. A feed-back approach to error control in finite element methods: Basic analysis and examples. East-West J. Numer. Math., 4:237-264, 1996.

9.
R. Becker and R. Rannacher. An optimal control approach to error estimation and mesh adaptation in finite element methods. Acta Numerica, Vol. 10, (A. Iserles, ed.) pp.1-101, Cambridge University Press, 2001.

10.
P. Binev, W. Dahmen, and R. DeVore. Adaptive finite element methods with convergence rates. Numerische Mathematik, 97(2):219-268, 2004.

11.
A. Cohen, W. Dahmen, and R. DeVore. Adaptive wavelet methods for elliptic operator equations--Convergence rates. Math. Comp., 70:22-75, 2001.

12.
K. Eriksson, D. Estep, P. Hansbo, and C. Johnson. Introduction to adaptive methods for differential equations. Acta Numerica, Vol. 4 (A. Iserles, ed.), pp.105-158, Cambridge University Press, 1995.

13.
K. Eriksson and C. Johnson. An adaptive finite element method for linear elliptic problems. Math. Comp., 50:361-383, 1988.

14.
K. Eriksson and C. Johnson. Adaptive finite element methods for parabolic problems, I: linear model problem. SIAM J. Numer. Anal., 28:43-77, 1991.

15.
M.B. Giles and E. Süli. Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality. Acta Numerica, Vol. 11 (A. Iserles, ed.), pp.145-236, Cambridge University Press, 2002.

16.
C. Johnson. Adaptive finite element methods for diffusion and convection problems. Comput. Methods Appl. Mech. Eng., 82:301-322, 1990.

17.
L. Machiels, A.T. Patera, and J. Peraire. Output bound approximation for partial differential equations; applications to the incompressible Navier-Stokes equations. In S. Biringen, editor, Industrial and Environmental Applications of Direct and Large Eddy Numerical Simulation. Springer, Berlin, Heidelberg, New York, 1998.

18.
P. Morin, R. Nochetto, and K. Siebert. Data oscillation and convergence of adaptive FEM. SIAM J. Numer. Anal., 38:466-488, 2000.

19.
J.T. Oden and S. Prudhomme. On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors. Comput. Methods Appl. Mech. Eng., 176:313-331, 1999.

20.
M. Paraschivoiou and A.T. Patera. Hierarchical duality approach bounds for the outputs of partial differential equations. Comput. Methods Appl. Mech. Eng., 158:389-407, 1998.

21.
R. Verfürth. A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley/Teubner, New York, Stuttgart, 1996.



Automatic sequences Theory applications generalizations, by Jean-Paul Allouche and Jeffrey Shallit
Cambridge University Press, Cambridge, 2003, xvi+571, $50.00
2000 Mathematics Subject Classification. Primary 11B85, 11Z05, 37A45, 37B10, 68Q45, 68R15, 94A45

Reviewed by: Alf van der Poorten
Affiliation: Centre for Number Theory Research 1 Bimbil Place, Killara Sydney, NSW 2071, Australia
E-mail address: alf@math.mq.edu.au

Practical extrapolation methods theory and applications, by Avram Sidi
Cambridge Monographs on Applied and Computational Mathematics, vol. 10, Cambridge University Press, Cambridge, 2003, xxii+519, $95.00
2000 Mathematics Subject Classification. Primary 40A05, 40A10, 40A25, 40A30, 40B05, 40G05, 41A20, 41A21, 41A25, 41A55, 41A58, 41A60, 65B05, 65B10, 65B15, 65D25, 65D30, 65R10, 65R20

Reviewed by: David Levin
Affiliation: Tel Aviv University

The Lanczos method evolution and application, by Louis Komzsik
Software, Environments, and Tools, vol. 15, SIAM, Philadelphia, PA, 2003, xii+87, $42.00
2000 Mathematics Subject Classification. Primary 65F15, 65F50

Reviewed by: Karl Meerbergen

Finite element methods for Maxwell s equations, by Peter Monk
Numerical Mathematics and Scientific Computation, Oxford University Press, New York, 2003, xiv+450, hardcover, $119.50
2000 Mathematics Subject Classification. Primary 65N30, 78A25, 78M10

Reviewed by: Ronald H. W. Hoppe
Affiliation: University of Houston University of Augsburg

References:

1.
Bossavit, A.; Electromagnétisme, en vue de la modélisation. Springer, Paris, 1993

2.
Bossavit, A.; Computational Electromagnetism. Variational Formulation, Complementarity, Edge Elements. Academic Press, San Diego, 1998

3.
Cessenat, M.; Mathematical Models in Electromagnetism. World Scientific, Singapore, 1996

4.
Colton, D., and Kress, R.; Inverse Acoustic and Electromagnetic Scattering Theory. 2nd Edition. Springer, Berlin-Heidelberg-New York, 1998

5.
Hiptmair, R.; Finite elements in computational electromagnetism, Acta Numerica 11, 237-339 (2002)

6.
Jin, J.-M.; The Finite Element Method in Electromagnetics. Wiley, New York, 1993

7.
Nédélec, J.-C.; Mixed finite elements in ${\mathbb R}^{3} $, Numer. Math. 35, 315-341 (1980)

8.
Nédélec, J.-C.; A new family of mixed finite elements in ${\mathbb R}^{3} $, Numer. Math. 50, 57-81 (1986)

9.
Nédélec, J.-C.; Acoustic and Electromagnetic Equations. Integral Representations for Harmonic Problems, Springer, Berlin-Heidelberg-New York, 2001

10.
Silvester, R.P., and Ferrari, R.L.; Finite Element Methods for Electrical Engineers. 3rd Edition. Cambridge University Press, Cambridge, 1996



Higher-order finite element methods, by Pavel Solín, Karel Segeth and Ivo Dolezel
Studies in Advanced Mathematics, Chapman & Hall/CRC, Boca Raton, FL, 2004, xxii+382, hardcover, $89.95
2000 Mathematics Subject Classification. Primary 65N30, 65N12, 65N15
with 1 CD-ROM (Windows, Macintosh, UNIX, and LINUX)

Reviewed by: Raytcho Lazarov
Affiliation: Department of MathematicsTexas A&M UniversityCollege Station, Texas


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