Enabling convergence of the iterated penalty Picard iteration with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e946" altimg="si2.svg"><mml:mrow><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> penalty parameter for incompressible Navier–Stokes via Anderson acceleration

This paper considers an enhancement of the classical iterated penalty Picard (IPP) method for incompressible Navier-Stokes equations, where we restrict our attention to $O(1)$ parameter, and Anderson acceleration (AA) is used significantly improve its convergence properties. After showing fixed point operator associated with IPP iteration Lipschitz continuous continuously (Frechet) differentiable, apply a recently developed general theory AA conclude that enhanced improves linear rate by gain factor underlying optimization problem. Results several challenging numerical tests are given show parameter 1 very effective solver.