05186nam 2200565Ia 450 001001700000005001700017010001800034010001800052010001800070010001800088035002600106035001600132035002100148035002200169035002300191035002500214035002300239035003000262100004000292101000800332135001800340200012200358205001200480210005500492215003100547300005200578311001900630320005100649327059400700327059101294327059401885327059102479327058903070327008903659330060503748606002604353606002304379615002704402615002404429676001204453686001604465700002704481801001104508801001104519801001104530906000904541912002104550996003904571997001004610991066719580332120230105233523.0 a0-19-163034-9 a1-283-42690-0 a9786613426901 a0-19-163033-0 a(CKB)2560000000079339 a(EBL)834727 a(OCoLC)772845035 a(MiAaPQ)EBC834727 a(Au-PeEL)EBL834727 a(CaPaEBR)ebr10523344 a(CaONFJC)MIL342690 a(EXLCZ)992560000000079339 a20110622d2011 uy 00 aeng aur|n|---|||||14aThe finite element methodb[electronic resource] ean introduction with partial differential equations /fA.J. Davies a2nd ed. aOxford ;aNew York cOxford University Pressd2011 a1 online resource (308 p.) aDescription based upon print version of record. a0-19-960913-6 aIncludes bibliographical references and index. aCover; 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 a3.1 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 a4.4 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 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 a6.2 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 a8.2 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 aAppendix E: Stehfest's formula and weights for numerical Laplace transform inversion aThe 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 aFinite element method aNumerical analysis 0aFinite element method. 0aNumerical analysis. a518/.25 aSK 9102rvk aDaviesb Alan J031003 0bMiAaPQ 1bMiAaPQ 2bMiAaPQ aBOOK a9910667195803321 aThe finite element method92748644 aUNINA