@Article{NMTMA-12-187, 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 = {2018}, volume = {12}, number = {1}, pages = {187--211}, abstract = {

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'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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0110}, url = {http://global-sci.org/intro/article_detail/nmtma/12697.html} }