The group finite element formulation

Abstract The introduction of trial solutions for groups of variables within a finite element formulation is shown to provide a significant economy with no loss of accuracy. For steady solutions of the two-dimensional Burgers' equations with linear rectangular elements the application of the group finite element to the convective term produces a threefold reduction in execution time with a small improvement in accuracy. Operation count estimates indicate even larger economies in three dimensions, or if higher-order nonlinearities occur, or if higher-order shape functions are used. Applications of the group formulation are described for inviscid and viscous, laminar and turbulent, separated and unseparated, and incompressible and compressible flows.

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