5 papers · 1 filter
Edge-based discretizations on triangulations in , with special attention to four-dimensional space
Nicholas Tufillaro, David M. Williams, Hiroaki Nishikawa
Many time-dependent problems in the field of computational fluid dynamics can be solved using space-time methods. However, such methods can encounter issues with computational cost…
Versatile mixed methods for weakly-compressible flows
Edward A. Miller, David M. Williams
Versatile mixed finite element methods were originally developed by Chen and Williams for isothermal incompressible flows in "Versatile mixed methods for the incompressible Navier-…
Error estimates for the interpolation and approximation of gradients and vector fields on protected Delaunay meshes in
David M. Williams, Mathijs Wintraecken
One frequently needs to interpolate or approximate gradients on simplicial meshes. Unfortunately, there are very few explicit mathematical results governing the interpolation or ap…
Quasi-optimal interpolation of gradients and vector-fields on protected Delaunay meshes in
David M. Williams, Mathijs Wintraecken
There are very few mathematical results governing the interpolation of functions or their gradients on Delaunay meshes in more than two dimensions. Unfortunately, the standard tech…
An explicit construction of optimized interpolation points on the 4-simplex
Trenton J. Gobel, David M. Williams
In this work, a family of symmetric interpolation points are generated on the four-dimensional simplex (i.e. the pentatope). These points are optimized in order to minimize the Leb…