@Article{NMTMA-12-1,
author = {},
title = {The Instability in the Dimensions of Spline Spaces over $T$-Meshes with Nested $T$-Cycles},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2019},
volume = {12},
number = {1},
pages = {187--211},
abstract = {<p style="text-align: justify;">This paper studies on the dimensions of spline spaces over some given $T$-meshes. Using the smoothing cofactor-conformality method, we study the instability in the dimensions of the spline spaces over $T$-meshes with 2-nested and 3-nested $T$-cycles. We define a singularity factor of each simple $T$-cycle, the instability and the structure&#39;s degeneration are associated with the singularity factors. In order to get a stable dimension formula over $T$-mesh with a $N$-nested $T$-cycle, a constraint on the $T$-mesh is introduced. Finally, a possible degeneration for a case of parallel $T$-cycles is illustrated.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2017-0110},
url = {https://global-sci.com/article/90391/the-instability-in-the-dimensions-of-spline-spaces-over-t-meshes-with-nested-t-cycles}
}