Introduction to finite and spectral element methods using MATLAB

THE FINITE ELEMENT METHOD IN ONE DIMENSION Steady diffusion with linear elements Variational formulation and weighted residuals Steady diffusion with quadratic elements Unsteady diffusion in one dimension One-dimensional convection One-dimensional convection-diffusion Beam bending Beam buckling HIGH-ORDER AND SPECTRAL ELEMENTS IN ONE DIMENSION Nodal bases Spectral interpolation Lobatto interpolation and element matrices Spectral code for steady diffusion Spectral code for unsteady diffusion Modal expansion THE FINITE ELEMENT METHOD IN TWO DIMENSIONS Convection-diffusion in two dimensions 3-node triangles Grid generation Code for Laplace's equation with the Dirichlet boundary condition in a disk-like domain Code for steady convection-diffusion with the Dirichlet boundary condition Code for Helmholtz's equation with the Neumann boundary condition Code for Laplace's equation with Dirichlet and Neumann boundary conditions Bilinear quadrilateral elements QUADRATIC AND SPECTRAL ELEMENTS IN TWO DIMENSIONS 6-node triangular elements Grid generation and finite element codes High-order triangle expansions High-order node distributions Modal expansion on the triangle Surface elements High-order quadrilateral elements APPLICATIONS IN SOLID AND FLUID MECHANICS Plane stress-strain analysis Finite element methods for plane stress/strain Plate bending Hermite triangles Finite element methods for plate bending Viscous flow Stokes flow Navier-Stokes flow FINITE AND SPECTRAL ELEMENT METHODS IN THREE DIMENSIONS Convection-diffusion in three dimensions 4-node tetrahedral elements High-order and spectral tetrahedral elements Hexahedral elements APPENDICES Function interpolation Orthogonal polynomials Linear solvers Mathematical supplement Element grid generation Glossary MATLAB primer References Index