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Finite element method. --- Finite element method --- eindige elementen --- torsie --- spanning --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Éléments finis, Méthode des --- Analyse numérique. --- Numerical analysis. --- Analyse numérique --- Éléments finis, Méthode des. --- Milieu continu

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Finite element method --- Méthode des éléments finis --- 519.6 --- 681.3 *G18 --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Computational mathematics. Numerical analysis. Computer programming --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Finite element method. --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Méthode des éléments finis --- Éléments finis, Méthode des --- Calcul des variations --- Éléments finis, Méthode des. --- Analyse structurale

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This expository book surveys the main concepts and recent advances in multiscale finite element methods. This monograph is intended for the broader audiences including engineers, applied scientists and those who are interested in multiscale simulations. The book is self-contained, starts from the basic concepts and proceeds to the latest developments in the field. Each chapter of the book starts with a simple introduction and the description of the proposed methods as well as with motivating examples. Numerical examples demonstrating the significance of the proposed methods are presented in each chapter. The book addresses mathematical and numerical issues in multiscale finite element methods and connects them to real-world applications. Narrative introduction provides a key to the book's organization and its scope. To make the presentation accessible to a broader audience, the analyses of the methods are given in the last chapter. Yalchin Efendiev is a Professor at Texas A&M University in College Station, Texas and Thomas Hou is the Charles Lee Powell Professor at California Institute of Technology in Pasadena, California.

Finite element method. --- Finite element method --- Numerical analysis. --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Amorphous semiconductors. --- Engineering. --- Earth sciences. --- Functional analysis. --- Mechanics. --- Mechanics, Applied. --- Fluid mechanics. --- Engineering, general. --- Numerical Analysis. --- Theoretical and Applied Mechanics. --- Engineering Fluid Dynamics. --- Earth Sciences, general. --- Functional Analysis. --- Electronics and optics of solids --- Mathematical analysis --- Numerical analysis --- Isogeometric analysis --- Mechanics, applied. --- Hydraulic engineering. --- Geography. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Cosmography --- Earth sciences --- World history --- Engineering, Hydraulic --- Engineering --- Fluid mechanics --- Hydraulics --- Shore protection --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Construction --- Industrial arts --- Technology --- Monograph --- Hydromechanics --- Continuum mechanics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Geosciences --- Environmental sciences --- Physical sciences

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Numerical solutions of differential equations --- Differential equations --- Difference equations --- Finite element method --- Numerical solutions --- Data processing --- -Differential equations --- -Finite element method --- -519.6 --- 681.3 *G18 --- 681.3*G17 --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Equations, Differential --- Bessel functions --- Calculus --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- -Data processing --- Computational mathematics. Numerical analysis. Computer programming --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- Data processing. --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff 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) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 517.91 Differential equations --- 519.6 --- Numerical solutions&delete& --- 517.91 --- Numerical solutions&delete&&delete& --- Differential equations - Numerical solutions - Data processing --- Difference equations - Numerical solutions - Data processing --- Finite element method - Data processing