MARC Record from harvard_bibliographic_metadata

LEADER: 03738cam a2200385Ia 4500
001 011413248-8
005 20140910154236.0
008 071206s2008 nyua b 001 0 eng d
010 $a 2007939977
020 $a9780387759333
020 $a0387759336
035 0 $aocn183259725
040 $aBTCTA$cBTCTA$dBAKER$dYDXCP$dOHX$dWAU$dDLC
050 00 $aQA379$b.B74 2008
100 1 $aBrenner, Susanne C.
245 14 $aThe mathematical theory of finite element methods /$cSusanne C. Brenner, L. Ridgway Scott.
250 $a3rd ed.
260 $aNew York, NY :$bSpringer,$cc2008.
300 $axvii, 397 p. :$bill. ;$c24 cm.
440 0 $aTexts in applied mathematics ;$v15
504 $aIncludes bibliographical references (p. [383]-391) and index.
505 0 $aBasic Concepts -- Sobolev Spaces -- Variational Formulation of Elliptic Boundary Value Problems -- The Construction of a Finite Element Space -- Polynomial Approximation Theory in Sobolev Spaces -- n-Dimensional Variational Problems -- Finite Element Multigrid Methods -- Additive Schwarz Preconditioners -- Max—norm Estimates -- Adaptive Meshes -- Variational Crimes -- Applications to Planar Elasticity -- Mixed Methods -- Iterative Techniques for Mixed Methods -- Applications of Operator-Interpolation Theory.
520 $aThis book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. The third edition contains four new sections: the BDDC domain decomposition preconditioner, convergence analysis of an adaptive algorithm, interior penalty methods and Poincara\'e-Friedrichs inequalities for piecewise W 1_p functions. New exercises have also been added throughout. The initial chapter provides an introducton to the entire subject, developed in the one-dimensional case. Four subsequent chapters develop the basic theory in the multidimensional case, and a fifth chapter presents basic applications of this theory.
520 $aSubsequent chapters provide an introduction to: - multigrid methods and domain decomposition methods - mixed methods with applications to elasticity and fluid mechanics - iterated penalty and augmented Lagrangian methods - variational "crimes" including nonconforming and isoparametric methods, numerical integration and interior penalty methods - error estimates in the maximum norm with applications to nonlinear problems - error estimators, adaptive meshes and convergence analysis of an adaptive algorithm - Banach-space operator-interpolation techniques The book has proved useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory and numerical analysis, while building upon and applying basic techniques of real variable theory. It can also be used for courses that emphasize physical applications or algorithmic efficiency.
520 $aReviews of earlier editions: "This book represents an important contribution to the mathematical literature of finite elements. It is both a well-done text and a good reference." (Mathematical Reviews, 1995) "This is an excellent, though demanding, introduction to key mathematical topics in the finite element method, and at the same time a valuable reference and source for workers in the area." (Zentralblatt, 2002)
650 0 $aBoundary value problems$xNumerical solutions.
650 0 $aFinite element method$xMathematics.
650 0 $aComputer science$xMathematics.
650 0 $aEngineering.
650 0 $aFunctional analysis.
650 0 $aMathematics.
650 0 $aMechanics, applied.
700 1 $aScott, L. Ridgway.
988 $a20080320
906 $0OCLC