Unified Isoparametric 3D LagrangeFinite Elements
Marcin Ma\'zdziarz;  

doi:10.3970/cmes.2010.066.001
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 66, No. 1, pp. 1-24, 2010
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Keywords Finite element method, Isoparametric elements, Numerical integration
Abstract The paper presents unified approach to 3D isoparametric Lagrange brick, tetra, and prism finite elements. All shape functions, linear, quadratic and cubic, are depicted in one Cartesian orthogonal coordinate system x,y,z regardless of the type of element. This allows one to use a single transformation rule to calculate global derivatives and a second for integration. Proper numerical Gauss quadratures for these isoparametric elements in a unified approach are presented additionally.
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