One Fewer Quadrature Point and the Solution Blew Up — DG's Integration Floor and the Taylor Basis
·8 min read
The minimum number of Gauss points in a DG cell integral is set by the degree of the integrand, not by the mesh. Going from three points to two changes nothing; going to one destroys the scheme.
Two Philosophies for Triangulating a Point Cloud — Bowyer–Watson and Advancing Front
·7 min read
Reproducing the two pillars of unstructured mesh generation, Delaunay and AFT, in code
The Fake Extrema a Second-Order Reconstruction Invents on Unstructured Grids — Barth–Jespersen and Venkatakrishnan Limiters
·6 min read
Slope limiters that tame the overshoot of second-order unstructured FVM
When the Mesh Skews, the Laplacian Leaks — Non-Orthogonal Diffusion Correction
·5 min read
Splitting the unstructured diffusion term into orthogonal plus correction, three ways
Saving Gradients on Unstructured Grids — Moving Least-Squares Approximation
·5 min read
A local polynomial fit that recovers both values and derivatives from scattered points
Delaunay Triangulation — the Empty-Circumcircle Rule and Bowyer–Watson Insertion
·6 min read
Why an unstructured mesh repairs itself when you drop in one point
[Paper Review] Beating the Storm Clock — Casulli–Walters (2000) Semi-Implicit Shallow Water on Unstructured Orthogonal Grids
·5 min read
A shallow-water algorithm that stays stable at large time steps