  The weak Galerkin (WG) methods have been introduced in the references [11,
16] for solving the biharmonic equation. The purpose of this paper is to
develop an algorithm to implement the WG methods effectively. This can be
achieved by eliminating local unknowns to obtain a global system with
significant reduction of size. In fact, this reduced global system is
equivalent to the Schur complements of the WG methods. The unknowns of the
Schur complement of the WG method are those defined on the element boundaries.
The equivalence of the WG method and its Schur complement is established. The
numerical results demonstrate the effectiveness of this new implementation
technique.
