$$C^1$$-Conforming Quadrilateral Spectral Element Method for Fourth-Order Equations

Abstract

In this talk, we propose a C¹-conforming quadrilateral spectral element method for fourth order partial differential equations. The approximation space is constituted by those globally C¹-continuous functions, which are essentially rational polynomials on each physical quadrilateral mapped from polynomials on the reference square by using bilinear transformations. So we first concentrate on the construction the shape functions of an arbitrary order on arbitrary quadrilateral meshes. The quadrilateral spectral element approximation scheme is then established with a brief explanation of the implementation. Numerical experiments are illustrated to demonstrate the accuracy and efficiency of our proposed method.