Introduction to Finite and Spectral Element Methods Using MATLAB

Introduction to Finite and Spectral Element Methods Using MATLAB

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Why another book on the finite element method? There are currently more than 200 books in print with "Finite Element Method" in their titles. Many are devoted to special topics or emphasize error analysis and numerical accuracy. Others stick to the fundamentals and do little to describe the development and implementation of algorithms for solving real-world problems. Introduction to Finite and Spectral Element Methods Using MATLAB provides a means of quickly understanding both the theoretical foundation and practical implementation of the finite element method and its companion spectral element method. Written in the form of a self-contained course, it introduces the fundamentals on a need-to-know basis and emphasizes algorithm development and computer implementation of the essential procedures. Firmly asserting the importance of simultaneous practical experience when learning any numerical method, the author provides FSELIB: a software library of user-defined MATLAB functions and complete finite and spectral element codes. FSELIB is freely available for download from http://dehesa.freeshell.org, which is also a host for the book, providing further information, links to resources, and FSELIB updates. The presentation is suitable for both self-study and formal course work, and its state-of-the-art review of the field make it equally valuable as a professional reference. With this book as a guide, you immediately will be able to run the codes as given and graphically display solutions to a wide variety of problems in heat transfer and solid, fluid, and structural mechanics.show more

Product details

  • Hardback | 680 pages
  • 160 x 236 x 40mm | 1,102.24g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 96 black & white illustrations, 18 black & white tables
  • 1584885297
  • 9781584885290

Table of contents

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 Indexshow more

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