Ebook: A Finite Element Primer for Beginners: The Basics
Author: Tarek I. Zohdi (auth.)
- Genre: Mathematics // Computational Mathematics
- Tags: Continuum Mechanics and Mechanics of Materials, Engineering Fluid Dynamics, Complexity, Computational Science and Engineering, Mathematical Modeling and Industrial Mathematics, Numerical and Computational Physics
- Series: SpringerBriefs in Applied Sciences and Technology
- Year: 2015
- Publisher: Springer International Publishing
- Edition: 1
- Language: English
- pdf
The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:
(1) Weighted residual methods and Galerkin approximations,
(2) A model problem for one-dimensional linear elastostatics,
(3) Weak formulations in one dimension,
(4) Minimum principles in one dimension,
(5) Error estimation in one dimension,
(5) Construction of Finite Element basis functions in one dimension,
(6) Gaussian Quadrature,
(7) Iterative solvers and element by element data structures,
(8) A model problem for three-dimensional linear elastostatics,
(9) Weak formulations in three dimensions,
(10) Basic rules for element construction in three-dimensions,
(11) Assembly of the system and solution schemes,
(12) Assembly of the system and solution schemes,
(13) An introduction to time-dependent problems and
(14) A brief introduction to rapid computation based on domain decomposition and basic parallel processing.
The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:
(1) Weighted residual methods and Galerkin approximations,
(2) A model problem for one-dimensional linear elastostatics,
(3) Weak formulations in one dimension,
(4) Minimum principles in one dimension,
(5) Error estimation in one dimension,
(5) Construction of Finite Element basis functions in one dimension,
(6) Gaussian Quadrature,
(7) Iterative solvers and element by element data structures,
(8) A model problem for three-dimensional linear elastostatics,
(9) Weak formulations in three dimensions,
(10) Basic rules for element construction in three-dimensions,
(11) Assembly of the system and solution schemes,
(12) Assembly of the system and solution schemes,
(13) An introduction to time-dependent problems and
(14) A brief introduction to rapid computation based on domain decomposition and basic parallel processing.