This paper focuses on decoupled finite element methods for the fourth-order exterior differential equation. Based on differential complexes and the Helmholtz decomposition, the fourth-order exterior differential equation is decomposed into two second-order exterior differential equations and one generalized Stokes equation. A family of conforming finite element methods are developed for the decoupled formulation. Numerical results are provided for verifying the decoupled finite element methods of the biharmonic equation in three dimensions.

翻译：本文聚焦于四阶外微分方程的分离有限元方法。基于微分复形与亥姆霍兹分解，四阶外微分方程被分解为两个二阶外微分方程与一个广义斯托克斯方程。针对分离后的方程组，发展了一类协调有限元方法。通过三维双调和方程的数值算例验证了所提出的分离有限元方法的有效性。