Residuals ``bottom out''

The bottoming out may be due to:

• normal truncation error in finite precision arithmetic. If this is the case, the update norm (equation 4.42) will usually provide a reasonable convergence condition, but the tolerances used to compute that norm may have to be relaxed for some fields (section 2.3.4).
• an incorrect system of equations. Too many boundary conditions may lead to an overconstrained system of nonlinear equations in which you can only hope to minimize the residual, not reduce it to zero.
• if the bottoming out occurs along with threshold adjustments, this may be an indication of sign flips inherent in the timestepping algorithm. Approaches to overcoming this problem are discussed in section 4.5.