Cover -- Frontmatter -- Half Title Page -- Title Page -- Copyright -- Contents -- Preface -- Features of the text and accompanying resources -- Notation -- 1. Introduction -- 1.1 Finite element methods -- 1.2 Capabilities of FEA -- 1.3 Outline of finite element procedures -- 1.4 Assembly into the system equations -- 1.5 Error concepts -- 1.6 Exercises -- 1.7 Bibliography -- 2. Mathematical preliminaries -- 2.1 Introduction -- 2.2 Linear spaces and norms -- 2.3 Sobolev norms -- 2.4 Dual problem, self-adjointness -- 2.5 Weighted residuals -- 2.6 Boundary condition terms -- 2.7 Adding more unknowns -- 2.8 Numerical integration -- 2.9 Integration by parts -- 2.10 Finite element model problem -- 2.11 Continuous nodal flux recovery -- 2.12 A one-dimensional example error analysis -- 2.13 General boundary condition choices -- 2.14 General matrix partitions -- 2.15 Elliptic boundary value problems -- 2.16 Initial value problems -- 2.17 Eigen-problems -- 2.18 Equivalent forms -- 2.19 Exercises -- 2.20 Bibliography -- 3. Element interpolation and local coordinates -- 3.1 Introduction -- 3.2 Linear interpolation -- 3.3 Quadratic interpolation -- 3.4 Lagrange interpolation -- 3.5 Hermitian interpolation -- 3.6 Hierarchical interpolation -- 3.7 Space-time interpolations -- 3.8 Nodally exact interpolations -- 3.9 Interpolation error -- 3.10 Gradient estimates -- 3.11 Exercises -- 3.12 Bibliography -- 4. One-dimensional integration -- 4.1 Introduction -- 4.2 Local coordinate Jacobian -- 4.3 Exact polynomial integration -- 4.4 Numerical integration -- 4.5 Variable Jacobians -- 4.6 Exercises -- 4.7 Bibliography -- 5. Error estimates for elliptic problems -- 5.1 Introduction -- 5.2 Error estimates -- 5.3 Hierarchical error indicator -- 5.4 Flux balancing error estimates -- 5.5 Element adaptivity -- 5.6 H-adaptivity -- 5.7 P-adaptivity -- 5.8 HP-adaptivity.

5.9 Exercises -- 5.10 Bibliography -- 6. Super-convergent patch recovery -- 6.1 Patch implementation database -- 6.2 SCP nodal flux averaging -- 6.3 Computing the SCP element error estimates -- 6.4 Hessian matrix -- 6.5 Exercises -- 6.6 Bibliography -- 7. Variational methods -- 7.1 Introduction -- 7.2 Structural mechanics -- 7.3 Finite element analysis -- 7.4 Continuous elastic bar -- 7.5 Thermal loads on a bar -- 7.6 Reaction flux recovery for an element -- 7.7 Heat transfer in a rod -- 7.8 Element validation -- 7.9 Euler's equations of variational calculus -- 7.10 Exercises -- 7.11 Bibliography -- 8. Cylindrical analysis problems -- 8.1 Introduction -- 8.2 Heat conduction in a cylinder -- 8.3 Cylindrical stress analysis -- 8.4 Exercises -- 8.5 Bibliography -- 9. General interpolation -- 9.1 Introduction -- 9.2 Unit coordinate interpolation -- 9.3 Natural coordinates -- 9.4 Isoparametric and subparametric elements -- 9.5 Hierarchical interpolation -- 9.6 Differential geometry -- 9.7 Mass properties -- 9.8 Interpolation error -- 9.9 Element distortion -- 9.10 Space-time interpolation -- 9.11 Exercises -- 9.12 Bibliography -- 10. Integration methods -- 10.1 Introduction -- 10.2 Unit coordinate integration -- 10.3 Simplex coordinate integration -- 10.4 Numerical integration -- 10.5 Typical source distribution integrals -- 10.6 Minimal, optimal, reduced and selected integration -- 10.7 Exercises -- 10.8 Bibliography -- 11. Scalar fields -- 11.1 Introduction -- 11.2 Variational formulation -- 11.3 Element and boundary matrices -- 11.4 Linear triangular element -- 11.5 Linear triangle applications -- 11.6 Bilinear rectangles -- 11.7 General 2-d elements -- 11.8 Numerically integrated arrays -- 11.9 Strong diagonal gradient SCP test case -- 11.10 Orthotropic conduction -- 11.11 Axisymmetric conductions -- 11.12 Torsion -- 11.13 Introduction to linear flows.

11.14 Potential flow -- 11.15 Axisymmetric plasma equilibria -- 11.16 Slider bearing lubrication -- 11.17 Transient scalar fields -- 11.18 Exercises -- 11.19 Bibliography -- 12. Vector fields -- 12.1 Introduction -- 12.2 Displacement based stress analysis summary -- 12.3 Planar models -- 12.4 Matrices for the constant strain triangle (CST) -- 12.5 Stress and strain transformations -- 12.6 Axisymmetric solid stress -- 12.7 General solid stress -- 12.8 Anisotropic materials -- 12.9 Circular hole in an infinite plate -- 12.10 Dynamics of solids -- 12.11 Exercises -- 12.12 Bibliography -- Index.