2 research outputs found
Provably size-guaranteed mesh generation with superconvergence
The properties and applications of superconvergence on size-guaranteed
Delaunay triangulation generated by bubble placement method (BPM), are studied
in this paper. First, we derive a mesh condition that the difference between
the actual side length and the desired length is as small as . Second, the superconvergence estimations
are analyzed on linear and quadratic finite element for elliptic boundary value
problem based on the above mesh condition. In particular, the mesh condition is
suitable for many known superconvergence estimations of different equations.
Numerical tests are provided to verify the theoretical findings and to exhibit
the superconvergence property on BPM-based grids
Fast variable density 3-D node generation
Mesh-free solvers for partial differential equations perform best on
scattered quasi-uniform nodes. Computational efficiency can be improved by
using nodes with greater spacing in regions of less activity. We present an
advancing front type method to generate variable density nodes in 2-D and 3-D
with clear generalization to higher dimensions. The exhibited cost of
generating a node set of size in 2-D and 3-D with the present method is
O(N)