An improved penalty method for power-law Stokes problems

For the numerical approximation of fluid flow phenomena, it is often highly desirable to decouple the equations defining conservation of momentum and conservation of mass by using a penalty function method. The current penalty function methods for power-law Stokes fluids converge at a sublinear rate with respect to the penalty parameter. In this article, we show theoretically and numerically that a linear penalty function approximation to a power-law Stokes problem yields a higher-order accuracy over the known nonlinear penalty method. Theoretically, finite element approximation of the linear penalty function method is shown to satisfy an improved order of approximation with respect to the penalty parameter. The numerical experiments presented in the paper support the theoretical results and satisfy a linear order of approximation.