A Stationary Formulation of the Space-time Finite Element Method

Abstract In this work, an unconditionally stable space-time finite element method is derived in its stationary form (the discretization is time invariant), [1] , [2] , [3] , [4] , [5] , [6] . The method formulation is solely displacement-based. An explicit or implicit integration scheme is obtained depending on the assumed parameters. The method's stability criterion has been derived. Assumed factors determine whether the method is conditionally or unconditionally stable. The precision of the solution has been subject to evaluation and the method's algorithm has been given. The presented method has been compared with Newmark's method [7] (a popular method of the equation of motion integration). The generalization presented in this paper is in analogy to the generalization in paper [8] and serves only as a reminder of this major work.