We examine Proportional-Integral- Derivative (PID) feedback control to enhance algorithm performance via parameter adap- tion. Of particular interest is use in branch- following algorithms applicable to turning point and bifurcation problems. Results of numeri- cal experiments are described for finite element approximation of a benchmark Navier-Stokes problem and for the classical Bratu reaction- diffusion problem. Continuation techniques provide a means of extending the range of flows for which a so- lution can be computed using a given nonli-
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