A family of \(C^1\) quadrilateral finite elements (Q824318)

This article discusses a family of \(C^1\) quadrilateral finite elements which define global \(C^1\) spaces over a general quadrilateral mesh with vertices of arbitrary valency. The proposed method allows the simple design of polynomial as well as of spline elements. The authors introduced a simple and local basis for the \(C^1\) quadrilateral space and obtained explicit formulas for the Bézier or spline coefficients of the basis functions. Optimal error estimates are also deduced. Numerical experiments included in the article support the theoretical findings and show the suitability of the proposed approximation methods to fourth-order PDEs.