@Article{CiCP-21-835,
author = {Wu , MengMourrain , BernardGalligo , André and Nkonga , Boniface},
title = {Hermite Type Spline Spaces over Rectangular Meshes with Complex Topological Structures},
journal = {Communications in Computational Physics},
year = {2018},
volume = {21},
number = {3},
pages = {835--866},
abstract = {<p style="text-align: justify;">Motivated by the magneto hydrodynamic (MHD) simulation for Tokamaks
with Isogeometric analysis, we present splines defined over a rectangular mesh with a
complex topological structure, i.e., with extraordinary vertices. These splines are piecewise
polynomial functions of bi-degree (d,d) and $C^r$ parameter continuity. And we
compute their dimension and exhibit basis functions called Hermite bases for bicubic
spline spaces. We investigate their potential applications for solving partial differential
equations (PDEs) over a physical domain in the framework of Isogeometric analysis.
For instance, we analyze the property of approximation of these spline spaces for the $L^2$-norm; we show that the optimal approximation order and numerical convergence
rates are reached by setting a proper parameterization, although the fact that the basis
functions are singular at extraordinary vertices.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2016-0030},
url = {http://global-sci.org/intro/article_detail/cicp/11262.html}
}