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[null,"1.","Record Nr.",null,"UNINA9910465743103321"]
[null,null,"Autore",null,"Davies Alan J"]
[null,null,"Titolo",null,"The finite element method [[electronic resource] ] : an introduction with partial differential equations / / A.J. Davies"]
[null,null,"Pubbl/distr/stampa",null,"Oxford ; ; New York, : Oxford University Press, 2011"]
[null,null,"ISBN",null,"1-283-42690-0"]
[{"$nulls":4},"9786613426901"]
[{"$nulls":4},"0-19-163033-0"]
[null,null,"Edizione",null,"[2nd ed.]"]
[null,null,"Descrizione fisica",null,"1 online resource (308 p.)"]
[null,null,"Disciplina",null,"518/.25"]
[null,null,"Soggetti",null,"Finite element method"]
[{"$nulls":4},"Numerical analysis"]
[{"$nulls":4},"Electronic books."]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Cover; Contents; 1 Historical introduction; 2 Weighted residual and variational methods; 2.1 Classification of differential operators; 2.2 Self-adjoint positive definite operators; 2.3 Weighted residual methods; 2.4 Extremum formulation: homogeneous boundary conditions; 2.5 Non-homogeneous boundary conditions; 2.6 Partial differential equations: natural boundary conditions; 2.7 The Rayleigh-Ritz method; 2.8 The 'elastic analogy' for Poisson's equation; 2.9 Variational methods for time-dependent problems; 2.10 Exercises and solutions; 3 The finite element method for elliptic problems"]
[{"$nulls":4},"3.1 Difficulties associated with the application of weighted residual methods3.2 Piecewise application of the Galerkin method; 3.3 Terminology; 3.4 Finite element idealization; 3.5 Illustrative problem involving one independent variable; 3.6 Finite element equations for Poisson's equation; 3.7 A rectangular element for Poisson's equation; 3.8 A triangular element for Poisson's equation; 3.9 Exercises and solutions; 4 Higher-order elements: the isoparametric concept; 4.1 A two-point boundary-value problem; 4.2 Higher-order rectangular elements; 4.3 Higher-order triangular elements"]
[{"$nulls":4},"4.4 Two degrees of freedom at each node4.5 Condensation of internal nodal freedoms; 4.6 Curved boundaries and higher-order elements: isoparametric elements; 4.7 Exercises and solutions; 5 Further topics in the finite element method; 5.1 The variational approach; 5.2 "]
[{"$nulls":4},"Collocation and least squares methods; 5.3 Use of Galerkin's method for time-dependent and non-linear problems; 5.4 Time-dependent problems using variational principles which are not extremal; 5.5 The Laplace transform; 5.6 Exercises and solutions; 6 Convergence of the finite element method; 6.1 A one-dimensional example"]
[{"$nulls":4},"6.2 Two-dimensional problems involving Poisson's equation6.3 Isoparametric elements: numerical integration; 6.4 Non-conforming elements: the patch test; 6.5 Comparison with the finite difference method: stability; 6.6 Exercises and solutions; 7 The boundary element method; 7.1 Integral formulation of boundary-value problems; 7.2 Boundary element idealization for Laplace's equation; 7.3 A constant boundary element for Laplace's equation; 7.4 A linear element for Laplace's equation; 7.5 Time-dependent problems; 7.6 Exercises and solutions; 8 Computational aspects; 8.1 Pre-processor"]
[{"$nulls":4},"8.2 Solution phase8.3 Post-processor; 8.4 Finite element method (FEM) or boundary element method (BEM)?; Appendix A: Partial differential equation models in the physical sciences; A.1 Parabolic problems; A.2 Elliptic problems; A.3 Hyperbolic problems; A.4 Initial and boundary conditions; Appendix B: Some integral theorems of the vector calculus; Appendix C: A formula for integrating products of area coordinates over a triangle; Appendix D: Numerical integration formulae; D.1 One-dimensional Gauss quadrature; D.2 Two-dimensional Gauss quadrature; D.3 Logarithmic Gauss quadrature"]
[{"$nulls":4},"Appendix E: Stehfest's formula and weights for numerical Laplace transform inversion"]
[null,null,null,"Sommario/riassunto","The finite element method is a technique for solving problems in applied science and engineering. The essence of this book is the application of the finite element method to the solution of boundary and initial-value problems posed in terms of partial differential equations. The method is developed for the solution of Poisson's equation, in a weighted-residual context, and then proceeds to time-dependent and nonlinear problems. The relationship with the variational approach is alsoexplained. This book is written at an introductory level, developing all the necessary concepts where required. Co"]