TY - JOUR
T1 - The Instability in the Dimensions of Spline Spaces over $T$-Meshes with Nested $T$-Cycles
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 187
EP - 211
PY - 2018
DA - 2018/09
SN - 12
DO - http://doi.org/10.4208/nmtma.OA-2017-0110
UR - https://global-sci.org/intro/article_detail/nmtma/12697.html
KW - 
AB - <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>