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REVIEWS AND DESCRIPTIONS OF TABLES AND BOOKS
Book reviews do not contain an abstract.
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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
, Numer. Math. 35, 315-341 (1980) - 8.
- Nédélec, J.-C.; A new family of mixed finite elements in
, 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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