Before revision:  These semi-discrete and fully-discrete schemes are proved to preserve the discrete averaged energy evolution law , In particular, we also prove that the proposed fully-discrete schemes exactly inherit the averaged energy evolution law almost surely if the considered model is driven by additive noise.
After revision:  These semi-discrete and fully-discrete schemes are proved to preserve the discrete averaged energy evolution law . In particular, we also prove that the proposed fully-discrete schemes exactly inherit the averaged energy evolution law almost surely if the considered model is driven by additive noise.