Finite Element AnalysisAn updated and comprehensive review of the theoretical foundation of the finite element methodThe revised and updated second edition of Finite Element Analysis: Method, Verification, and Validation offers a comprehensive review of the theoretical foundations of the finite element method and highlights the fundamentals of solution verification, validation, and uncertainty quantification. Written by noted experts on the topic, the book covers the theoretical fundamentals as well as the algorithmic structure of the finite element method. The text contains numerous examples and helpful exercises that clearly illustrate the techniques and procedures needed for accurate estimation of the quantities of interest. In addition, the authors describe the technical requirements for the formulation and application of design rules.Designed as an accessible resource, the book has a companion website that contains a solutions manual, PowerPoint slides for instructors, and a link to finite element software. This important text:* Offers a comprehensive review of the theoretical foundations of the finite element method* Puts the focus on the fundamentals of solution verification, validation, and uncertainty quantification* Presents the techniques and procedures of quality assurance in numerical solutions of mathematical problems* Contains numerous examples and exercisesWritten for students in mechanical and civil engineering, analysts seeking professional certification, and applied mathematicians, Finite Element Analysis: Method, Verification, and Validation, Second Edition includes the tools, concepts, techniques, and procedures that help with an understanding of finite element analysis.

1 Introduction to FEM 31.1 An introductory problem 61.2 Generalized formulation 91.2.1 The exact solution 91.2.2 The principle of minimum potential energy 141.3 Approximate solutions 161.3.1 The standard polynomial space 171.3.2 Finite element spaces in one dimension 201.3.3 Computation of the coefficient matrices 221.3.4 Computation of the right hand side vector 261.3.5 Assembly 271.3.6 Condensation 301.3.7 Enforcement of Dirichlet boundary conditions 301.4 Post-solution operations 331.4.1 Computation of the quantities of interest 331.5 Estimation of error in energy norm 371.5.1 Regularity 381.5.2 A priori estimation of the rate of convergence 381.5.3 A posteriori estimation of error 401.5.4 Error in the extracted QoI 461.6 The choice of discretization in 1D 471.6.1 The exact solution lies in Hk(I), k . 1 > p 471.6.2 The exact solution lies in Hk(I), k . 1