Decoupled mixed element schemes for fourth order problems
Provides a new framework for solving high-regularity problems with simpler discretizations, potentially benefiting computational mechanics and PDE solvers.
The paper develops a general process to transform fourth-order elliptic problems into decoupled systems using low-order finite elements, and applies it to the 3D bi-Laplacian equation to create mixed element schemes.
In this paper, we study decoupled mixed element schemes for fourth order problems. A general process is designed such that an elliptic problem on high-regularity space is transformed to a decoupled system with spaces of low order involved only and is further discretised by low-degree finite elements. The process can be fit for various fourth order problems, and is used in the remaining of the paper particularly for three-dimensional bi-Laplacian equation to conduct a family of mixed element discretisation schemes.