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001 978-0-387-75934-0
003 DE-He213
005 20161121231209.0
007 cr nn 008mamaa
008 100301s2008 xxu| s |||| 0|eng d
020 _a9780387759340
_9978-0-387-75934-0
024 7 _a10.1007/978-0-387-75934-0
_2doi
050 4 _aT57-57.97
072 7 _aPBW
_2bicssc
072 7 _aMAT003000
_2bisacsh
082 0 4 _a519
_223
100 1 _aBrenner, Susanne C.
_eauthor.
245 1 4 _aThe Mathematical Theory of Finite Element Methods
_h[electronic resource] /
_cby Susanne C. Brenner, L. Ridgway Scott.
264 1 _aNew York, NY :
_bSpringer New York,
_c2008.
300 _aXVIII, 400 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aTexts in Applied Mathematics,
_x0939-2475 ;
_v15
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. Subsequent 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. Reviews 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 _aMathematics.
650 0 _aFunctional analysis.
650 0 _aApplied mathematics.
650 0 _aEngineering mathematics.
650 0 _aComputer mathematics.
650 0 _aComputational intelligence.
650 0 _aMechanics.
650 0 _aMechanics, Applied.
650 1 4 _aMathematics.
650 2 4 _aApplications of Mathematics.
650 2 4 _aComputational Mathematics and Numerical Analysis.
650 2 4 _aComputational Intelligence.
650 2 4 _aTheoretical and Applied Mechanics.
650 2 4 _aFunctional Analysis.
700 1 _aScott, L. Ridgway.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387759333
830 0 _aTexts in Applied Mathematics,
_x0939-2475 ;
_v15
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-387-75934-0
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c509972
_d509972