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This 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)  .

Mathematics. --- Functional analysis. --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Computational intelligence. --- Mechanics. --- Mechanics, Applied. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Computational Intelligence. --- Theoretical and Applied Mechanics. --- Functional Analysis. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Engineering --- Engineering analysis --- Mathematical analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Mathematics --- Boundary value problems --- Finite element method --- Numerical solutions. --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Computer science --- Engineering. --- Mechanics, applied. --- Construction --- Industrial arts --- Technology --- Engineering Mechanics. --- Data processing.

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Numerical partial differential equations (PDEs) are an important part of numerical simulation, the third component of the modern methodology for science and engineering, besides the traditional theory and experiment. This volume contains papers that originated with the collaborative research of the teams that participated in the IMA Workshop for Women in Applied Mathematics: Numerical Partial Differential Equations and Scientific Computing in August 2014.

Partial differential equations --- Numerical analysis --- Mathematics --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- differentiaalvergelijkingen --- vormgeving --- informatica --- mineralen (chemie) --- simulaties --- externe fixatie (geneeskunde --- mijnbouw --- wiskunde --- numerieke analyse

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This 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 W1\_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.


Numerical solutions of differential equations --- Functional analysis --- finite element method --- computer-aided engineering --- CAE (computer aided engineering) --- Boundary conditions (Differential equations) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Boundary value problems --- Finite element method --- 519.6 --- 681.3 *G18 --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Numerical solutions --- Mathematics --- eindige elementen --- Numerical solutions. --- Mathematics. --- Computer mathematics. --- Computational intelligence. --- Mechanics. --- Mechanics, Applied. --- Functional analysis. --- Computational Mathematics and Numerical Analysis. --- Computational Intelligence. --- Theoretical and Applied Mechanics. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Computer mathematics --- Electronic data processing --- Boundary value problems - numerical solutions --- Finite element method - mathematics

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Functional analysis --- Classical mechanics. Field theory --- Computer. Automation --- toegepaste mechanica --- functies (wiskunde) --- informatica --- wiskunde --- algoritmen --- mechanica --- numerieke analyse

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• Reference Manager
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This 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 W1_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)

Functional analysis --- Classical mechanics. Field theory --- Computer. Automation --- toegepaste mechanica --- functies (wiskunde) --- informatica --- wiskunde --- algoritmen --- mechanica --- numerieke analyse