An operational procedure for the symbolic analysis of the finite element method

An operational procedure is presented for the symbolic analysis of different finite element discretizations which enables one to symbolically decouple the finite element equations and recover the corresponding limit differential equations which govern the finite element behavior. Comparison of the limit differential equations with the continuum differential equations succinctly manifests the component-wise discretization effects on element behavior such as the transverse shear element locking phenomenon exhibited by thin Co elements. The procedure is applied to the Hermitian approximation of the Sturm-Liouville equation and to the linear approximation of the Timoshenko beam.