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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.
List of contents
Weighted residuals and Galerkin's method for a generic 1-D problem.- A model problem: 1-D elastostatics.- A finite element implementation in one dimension.- Accuracy of the finite element method.- Element by element iterative solutions schemes.- Weak formulations in three dimensions.- A finite element implementation in three dimensions.- Accuracy of the finite element method.- Time-dependent problems.- Summary and advanced topics.
Report
"The book by Zohdi ... discusses the FEM 1D and 3D problems in linear elasticity. ... The book looks attractive ad is easy to read. ... this is a nice little elementary book on FEM, which has an attractive and non-intimidating form for the students beginning her/his FEM studies, or for individuals whose areas of interest is different but desire to get a taste of what FEM is all about." (Dan Givoli, IACM Expressions, Issue 39, July, 2016)
