  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.
