Abstract: We all know the Lax Equivalence Theorem: Assuming consistency, convergence is equivalent to numerical stability. However, it is in practice very difficult to verify the numerical stability of a scheme while solving an evolution equation, especially if the equation is nonlinear and/or the scheme is complex. Consequently, a large gap exists between error analysis theory and numerical computation practice. We prove that one can use numerical smoothing to replace numerical stability in error estimation. As a property of the computed numerical solution, the numerical smoothing property can be monitored by a “smoothing indicator”.