A better consistency for low-order stabilized finite element methods Original Research Article

The standard implementation of stabilized finite element methods with a piece-wise function space of order lower than the highest derivative present in the partial differential equation often suffers from a weak consistency that can lead to reduced accuracy. The popularity of these low-order elements motivates the development of a new stabilization operator which globally reconstructs the derivatives not present in the local element function space. This new method is seen to engender a stronger consistency leading to better convergence and improved accuracy. Applications to the Navier—Stokes equations are given which illustrate the improvement at a negligible additional cost.