Decoupled finite element methods for a fourth-order exterior differential equation
Numerical Analysis
2025-02-20 v2 Numerical Analysis
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.
Cite
@article{arxiv.2410.09689,
title = {Decoupled finite element methods for a fourth-order exterior differential equation},
author = {Xuewei Cui and Xuehai Huang},
journal= {arXiv preprint arXiv:2410.09689},
year = {2025}
}
Comments
27 pages