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math.NA2023
Conforming Finite Element Function Spaces in Four Dimensions, Part II: The Pentatope and Tetrahedral Prism
David M. Williams, Nilima Nigam
In this paper, we present explicit expressions for conforming finite element function spaces, basis functions, and degrees of freedom on the pentatope and tetrahedral prism element…
math.NA2023
Conforming Finite Element Function Spaces in Four Dimensions, Part 1: Foundational Principles and the Tesseract
Nilima Nigam, David M. Williams
The stability, robustness, accuracy, and efficiency of space-time finite element methods crucially depend on the choice of approximation spaces for test and trial functions. This i…
math.NA2023★ 1 cited
Surface and hypersurface meshing techniques for space-time finite element methods
Jude T. Anderson, David M. Williams, Andrew Corrigan
A general method is introduced for constructing two-dimensional (2D) surface meshes embedded in three-dimensional (3D) space time, and 3D hypersurface meshes embedded in four-dimen…