A Finite Element Primer for Beginners

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<p>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:</p><p>(1) Weighted residual methods and Galerkin approximations,</p><p>(2) A model problem for one-dimensional linear elastostatics,</p><p>(3) Weak formulations in one dimension,</p><p>(4) Minimum principles in one dimension,</p><p>(5) Error estimation in one dimension,</p><p>(5) Construction of Finite Element basis functions in one dimension,</p><p>(6) Gaussian Quadrature,</p><p>(7) Iterative solvers and element by element data structures,</p><p>(8) A model problem for three-dimensional linear elastostatics,</p><p>(9) Weak formulations in three dimensions,</p><p>(10) Basic rules for element construction in three-dimensions,</p><p>(11) Assembly of the system and solution schemes,</p><p>(12) Assembly of the system and solution schemes,</p><p>(13) An introduction to time-dependent problems and</p><p>(14) A brief introduction to rapid computation based on domain decomposition and basic parallel processing.</p>

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