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Finite elements : theory and algorithms (2017)

Ganesan, Sashikumaar, ; Tobiska, L. 1950-

Cambridge :Cambridge University Press,

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UID:

almafu_9960117697202883

Umfang: 1 online resource (vi, 208 pages) : , digital, PDF file(s).

ISBN: 1-108-34421-6 , 1-108-23501-8

Serie: Cambridge--IISc series

Inhalt: Written in easy to understand language, this self-explanatory guide introduces the fundamentals of finite element methods and its application to differential equations. Beginning with a brief introduction to Sobolev spaces and elliptic scalar problems, the text progresses through an explanation of finite element spaces and estimates for the interpolation error. The concepts of finite element methods for parabolic scalar parabolic problems, object-oriented finite element algorithms, efficient implementation techniques, and high dimensional parabolic problems are presented in different chapters. Recent advances in finite element methods, including non-conforming finite elements for boundary value problems of higher order and approaches for solving differential equations in high dimensional domains are explained for the benefit of the reader. Numerous solved examples and mathematical theorems are interspersed throughout the text for enhanced learning.

Anmerkung: Title from publisher's bibliographic system (viewed on 05 Jan 2018). , Cover -- Finite Elements -- Title -- Copyright -- CONTENTS -- PREFACE -- CHAPTER 1: INTRODUCTION TO SOBOLEV SPACES -- 1.1 BANACH AND HILBERT SPACES -- 1.2 WEAK DERIVATIVES -- 1.3 SOBOLEV SPACES -- CHAPTER 2: ELLIPTIC SCALAR PROBLEMS -- 2.1 A GENERAL ELLIPTIC PROBLEM OF SECOND ORDER -- 2.2 WEAK SOLUTION -- 2.3 STANDARD GALERKIN METHOD -- 2.4 ABSTRACT ERROR ESTIMATE -- CHAPTER 3: FINITE ELEMENT SPACES -- 3.1 SIMPLICES AND BARYCENTRIC COORDINATES -- 3.2 SIMPLICIAL FINITE ELEMENTS AND LOCAL SPACES -- 3.3 CONSTRUCTION OF FINITE ELEMENT SPACES -- 3.4 THE CONCEPT OF MAPPED FINITE ELEMENTS: AFFINE MAPPINGS -- 3.5 FINITE ELEMENTS ON RECTANGULAR AND BRICK MESHES -- 3.6 MAPPED FINITE ELEMENTS: GENERAL BIJECTIVE MAPPINGS -- 3.7 MAPPED QK FINITE ELEMENT -- 3.8 ISOPARAMETRIC FINITE ELEMENTS -- 3.9 FURTHER EXAMPLES OF FINITE ELEMENT SPACES IN C0 AND C1 -- Serendipity element -- Argyris triangle -- Bell's triangle -- CHAPTER 4: INTERPOLATION AND DISCRETIZATION ERROR -- 4.1 TRANSFORMATION FORMULAS -- 4.2 AFFINE EQUIVALENT FINITE ELEMENTS -- 4.3 CANONICAL INTERPOLATION -- 4.4 LOCAL AND GLOBAL INTERPOLATION ERROR -- 4.5 IMPROVED L2 ERROR ESTIMATES BY DUALITY -- 4.6 INTERPOLATION OF LESS SMOOTH FUNCTIONS -- CHAPTER 5: BIHARMONIC EQUATION -- 5.1 DEFLECTION OF A THIN CLAMPED PLATE -- 5.2 WEAK FORMULATION OF THE BIHARMONIC EQUATION -- 5.3 CONFORMING FINITE ELEMENT METHODS -- The Bogner-Fox-Schmit rectangle -- The Hsieh-Clough-Tocher (HCT) triangle -- A C1 tetrahedral finite element -- 5.4 NONCONFORMING FINITE ELEMENT METHODS -- The rectangular Adini element -- The triangularMorley element -- A nonconforming tetrahedral element -- CHAPTER 6: PARABOLIC PROBLEMS -- 6.1 CONSERVATION OF ENERGY -- 6.2 A GENERAL PARABOLIC PROBLEM OF SECOND ORDER -- 6.3 WEAK FORMULATION OF INITIAL BOUNDARY VALUE PROBLEMS -- 6.4 SEMIDISCRETIZATION BY FINITE ELEMENTS -- 6.5 TIME DISCRETIZATION. , A-stability and L-stability -- Time-stepping methods -- Backward Euler method -- Crank-Nicolson method -- Fractional step θ-scheme -- Galerkin and Galerkin-Petrov time-stepping methods -- Discontinuous Galerkin time-stepping methods -- Continuous Galerkin-Petrov time-stepping methods -- 6.6 FINITE ELEMENTS FOR HIGH-DIMENSIONAL PARABOLIC PROBLEMS -- High-dimensional equation -- Operator-splitting techniques -- Lie-Trotter splitting -- Strang splitting -- CHAPTER 7: SYSTEMS IN SOLID MECHANICS -- 7.1 LINEAR ELASTICITY -- 7.2 MINDLIN-REISSNER PLATE -- CHAPTER 8: SYSTEMS IN FLUID MECHANICS -- 8.1 CONSERVATION OF MASS AND MOMENTUM -- Navier-Stokes problem -- Oseen problem -- Stokes problem -- 8.2 WEAK FORMULATION OF THE STOKES PROBLEM -- 8.3 CONFORMING DISCRETIZATIONS OF THE STOKES PROBLEM -- 8.4 NONCONFORMING DISCRETIZATIONS OF THE STOKES PROBLEM -- 8.5 THE NONCONFORMING CROUZEIX-RAVIART ELEMENT -- 8.6 FURTHER INF-SUP STABLE FINITE ELEMENT PAIRS -- Conforming triangular finite elements -- Conforming quadrilateral finite elements -- Nonconforming triangular finite elements -- Nonconforming quadrilateral finite elements -- Inf-sup stable finite elements in 3d -- Some special cases of inf-sup stable elements -- 8.7 EQUAL ORDER STABILIZED FINITE ELEMENTS -- 8.8 NAVIER-STOKES PROBLEM WITH MIXED BOUNDARY CONDITIONS -- 8.9 TIME DISCRETIZATION AND LINEARIZATION OF THE NAVIER-STOKES PROBLEM -- CHAPTER 9: IMPLEMENTATION OF THE FINITE ELEMENT METHOD -- 9.1 MESH HANDLING AND DATA STRUCTURE -- 9.2 NUMERICAL INTEGRATION -- Numerical quadrature for integrals over [−1, 1]d -- Numerical quadrature for simplex -- 9.3 SPARSE MATRIX STORAGE -- Compressed row storage (CRS) or compressed sparse row (CSR) format -- Compressed column storage (CCS) or compressed sparse column (CSC) format -- Block compressed row storage (BCRS) format -- Matrix stencil of a finite element space. , Retrieving a nonzero entry from a CSR format matrix -- Matrix vector multiplication -- 9.4 ASSEMBLING OF SYSTEM MATRICES AND LOAD VECTORS -- Assembling the system matrix of a scalar problem -- Assembling the system matrix of a vector-valued problem -- 9.5 INCLUSION OF BOUNDARY CONDITIONS -- Inclusion of Dirichlet type boundary conditions -- Inclusion of the Robin type boundary conditions -- Inclusion of the Navier-Slip boundary condition -- Handling L20 (Ω) pressure space -- Evaluating integrals with surface gradient -- 9.6 SOLUTION OF THE ALGEBRAIC SYSTEMS -- Direct solvers -- Iterative solvers -- 9.7 OBJECT-ORIENTED C++ PROGRAMMING -- Class and object in 1d finite element -- BIBLIOGRAPHY -- INDEX.

Weitere Ausg.: ISBN 1-108-41570-9

Sprache: Englisch

URL: https://doi.org/10.1017/9781108235013

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Finite elements : theory and algorithms (2017)

Ganesan, Sashikumaar [VerfasserIn] 1976- ; Tobiska, Lutz [VerfasserIn] 1950-

Cambridge : Cambridge University Press

zur Merkliste hinzufügen auf der Merkliste

Details

UID:

gbv_1015106862

Umfang: 1 Online-Ressource (viii, 208 Seiten)

ISBN: 9781108235013

Serie: Cambridge--IISc series

Anmerkung: Title from publisher's bibliographic system (viewed on 05 Jan 2018)

Weitere Ausg.: ISBN 9781108415705

Weitere Ausg.: Erscheint auch als Druck-Ausgabe Ganesan, Sashikumaar, 1976 - Finite elements Cambridge, United Kingdom : Cambridge University Press, 2017 ISBN 9781108415705

Weitere Ausg.: ISBN 1108415709

Sprache: Englisch

Fachgebiete: Mathematik

RVK:

SK 900

Schlagwort(e): Finite-Elemente-Methode ; Partielle Differentialgleichung ; Finite-Elemente-Methode ; Partielle Differentialgleichung

DOI: 10.1017/9781108235013

URL: Volltext

URL: Inhaltstext

Mehr zum Autor: Tobiska, Lutz 1950-

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