On the Full C_(1)-Q_(k) Finite Element Spaces on Rectangles and Cuboids  

作　　者：Shangyou Zhang 

机构地区：[1]Department of Mathematical Sciences,University of Delaware,Newark,Delaware 19716-2553,USA

出　　处：《Advances in Applied Mathematics and Mechanics》2010年第6期701-721,共21页应用数学与力学进展（英文）

摘　　要：We study the extensions of the Bogner-Fox-Schmit element to the whole family of Q_(k) continuously differentiable finite elements on rectangular grids,for all k≥3,in 2D and 3D.We show that the newly defined C_(1) spaces are maximal in the sense that they contain all C_(1)-Q_(k) functions of piecewise polynomials.We give examples of other extensions of C_(1)-Q_(k) elements.The result is consistent with the Strang’s conjecture(restricted to the quadrilateral grids in 2D and 3D).Some numerical results are provided on the family of C_(1) elements solving the biharmonic equation.

关 键 词：Differentiable finite element biharmonic equation Bogner-Fox-Schmit rectangle quadrilateral element hexahedral element Strang’s conjecture 

分 类 号：O17[理学—数学]