Variational space–time elements for large-scale systems

• Published in: Computer methods in applied mechanics and engineering Vol. 326; pp. 541 - 572
• Main Authors: Hesch, C., Schuß, S., Dittmann, M., Eugster, S.R., Favino, M., Krause, R.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-11-2017; Elsevier BV
• Subjects: Finite element analysis; Finite element method; Formulations; Galerkin; Galerkin method; IGA; Large-scale; Multigrid; Numerical analysis; Parallel; Partial differential equations; Shape functions; Spacetime; Space–time; IGA; Parallel; Space–time; Large-scale; Multigrid; Galerkin
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2017.08.020

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.