3 citations · 3 across the 2 of their papers we have counts for
8 papers
Interpolation Error Estimates for Harmonic Coordinates On Polytopes
Andrew Gillette, Alexander Rand
Interpolation error estimates in terms of geometric quality measures are established for harmonic coordinates on polytopes in two and three dimensions. First we derive interpolatio…
Construction of scalar and vector finite element families on polygonal and polyhedral meshes
Andrew Gillette, Alexander Rand, Chandrajit Bajaj
We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis…
Average Interpolation Under the Maximum Angle Condition
Alexander Rand
Interpolation error estimates needed in common finite element applications using simplicial meshes typically impose restrictions on the both the smoothness of the interpolated func…
Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons
Alexander Rand, Andrew Gillette, Chandrajit Bajaj
In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, doi:10.1007/s10444-011-9218-z], we prove interpolation error est…
Quadratic Serendipity Finite Elements on Polygons Using Generalized Barycentric Coordinates
Alexander Rand, Andrew Gillette, Chandrajit Bajaj
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon satisfying…
Improved Examples of Non-Termination for Ruppert's Algorithm
Alexander Rand
Improving the best known examples, two planar straight-line graphs which cause the non-termination of Ruppert's algorithm for a minimum angle threshold as low as 29.06 degrees are…