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We show that the fourth order accurate finite difference implementation ofcontinuous finite element method with tensor product of quadratic polynomialbasis is monotone thus satisfies the discrete maximum principle for solving ascalar variable coefficient equation $-\nabla\cdot(a\nabla u)+cu=f$ under asuitable mesh constraint.

On the monotonicity and discrete maximum principle of the finite difference implementation of $C^0$-$Q^2$ finite element method