Decoupled finite element methods for a fourth-order exterior differential equation

Xuewei Cui; Xuehai Huang

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arXiv · 2410.09689

Decoupled finite element methods for a fourth-order exterior differential equation

Xuewei Cui·Xuehai Huang

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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.

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Xuewei Cui, Xuehai Huang. 2024-10-13. Decoupled finite element methods for a fourth-order exterior differential equation. https://arxiv.org/abs/2410.09689

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