Author(s)

G. Dasgupta

Abstract

The key to the success of the finite element method is that the local test func- tions are based on element geometry alone— irrespective of the governing field equation. Originally, Courant proposed a scheme of (generalized) triangulation for second order elliptic partial differential equations where the domain in K" was divided into finite subregions of (n + 1)-vertices. Weights for Ritz' linear test functions which identically satisfy homogeneous differential equations were determined by minimizing an energy integral. "Computational experience" led Courant's mathematically well-founded method into two-dimensional quadrilat- eral subregions. Associated quadratic polynomial interpolants, intended for higher accuracy, do not satisfy the equilibrium equation pointwise or in the strong sense. MacNeal's theorem establ

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