  A novel nonlinear formulation of the finite element and Galerkin methods is
presented here, which leads to the Hadamard product expression of the resultant
nonlinear algebraic analogue. The presented formulation attains the advantages
of weak formulation in the standard finite element and Galerkin schemes and
avoids the costly repeated numerical integration of the Jacobian matrix via the
recently developed SJT product approach. This also provides possibility of the
nonlinear decoupling computations.
