Year: 2024
Type: preprint
Abstract: This paper proposes novel decoupled finite element methods for a 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 key advantage of this decoupled formulation is that it avoids the use of quotient spaces. 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.
Source: arXiv (Cornell University)
Authors: Cui, Xuewei, Huang, Xuehai
Institution: Shanghai University of Finance and Economics
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Award: G6678179562
OpenAlex ID: W4403578032