3 citations · 6 across the 9 of their papers we have counts for
9 papers
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…
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…
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…
Generalized Korn's Inequalities for Piecewise Vector Fields
David M. Williams, Qingguo Hong
The purpose of this paper is to construct a new class of discrete generalized Korn's inequalities for piecewise H2 vector fields in three-dimensional space. The resulting Korn's in…
Enabling four-dimensional conformal hybrid meshing with cubic pyramids
Miroslav S. Petrov, Todor D. Todorov, Gage S. Walters +2
The main purpose of this article is to develop a novel refinement strategy for four-dimensional hybrid meshes based on cubic pyramids. This optimal refinement strategy subdivides a…
A finite element discrete Boltzmann method for high Knudsen number flows
Karthik Ganeshan, David M. Williams
Simulations of the discrete Boltzmann Bhatnagar-Gross-Krook (BGK) equation are an important tool for understanding fluid dynamics in non-continuum regimes. Here, we introduce a dis…
Foundations of space-time finite element methods: polytopes, interpolation, and integration
Cory V. Frontin, Gage S. Walters, Freddie D. Witherden +3
The main purpose of this article is to facilitate the implementation of space-time finite element methods in four-dimensional space. In order to develop a finite element method in…
Versatile Mixed Methods for Non-Isothermal Incompressible Flows
Edward A. Miller, Xi Chen, David M. Williams
The purpose of this paper is to extend the versatile mixed methods originally developed by Chen and Williams for isothermal flows in "Versatile Mixed Methods for the Incompressible…
Versatile Mixed Methods for the Incompressible Navier-Stokes Equations
Xi Chen, David M. Williams
In the spirit of the "Principle of Equipresence" introduced by Truesdell & Toupin, The Classical Field Theories (1960), we use the full version of the viscous stress tensor which w…