We construct four variants of space‐time finite element discretizations based on linear tensor‐
product and simplex‐type finite elements. The resulting discretizations are continuous in …

A novel method is introduced for constructing two-dimensional (2D) surface meshes
embedded in three-dimensional (3D) space time and 3D hypersurface meshes embedded …

Recently, many advances have been done in the field of space-time finite element
discretizations for nonstationary partial differential equations. The temporal dimension leads …

This paper presents a space-time interface-fitted finite element method for solving a
parabolic advection-diffusion problem with a nonstationary interface. The jum** diffusion …

In the context of simulation‐based methods, multiple challenges arise, two of which are
considered in this work. As a first challenge, problems including time‐dependent …

In this work, we introduce a novel boundary‐conforming mesh‐update method that is
particularly designed for problems with large boundary displacements and topology …

Part 1 of this paper provides a comprehensive guide to generating unconstrained, simplicial,
four-dimensional (4D), hypervolume meshes. While a general procedure for constructing …

This paper addresses two problems needed to support four-dimensional (3 d+ t) spacetime
numerical simulations. The first contribution is a general algorithm for producing conforming …

In this paper, we present explicit expressions for conforming finite element function spaces,
basis functions, and degrees of freedom on the pentatope (the 4-simplex) and tetrahedral …

This paper highlights how unstructured space-time meshes can be used in production
engineering applications with moving domains. Unstructured space-time elements can …