@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 = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0030}, url = {http://global-sci.org/intro/article_detail/cicp/11262.html} }