Variational space–time elements for large-scale systems

In this paper, we introduce a new Galerkin based formulation for transient continuum problems, governed by partial differential equations in space and time. Therefore, we aim at a direct finite element discretization of the space–time, suitable for massive parallel analysis of the arising large-scale problem. The proposed formulation is applied to thermal, mechanical and fluid systems, as well as to a Kuramoto–Sivashinsky problem, representing the general class of higher-order formulations in material science using NURBS based shape functions. We verify whenever possible the conservation properties of the formulation. Finally, a series of examples demonstrate the applicability to all systems presented in this paper.