Local Projection Stabilization Method for Incompressible Flow Problems

This paper analyzes Local Projection Stabilization (LPS) methods for the solution of Stokes problem using equal order finite elements. Their convergence, stability and accuracy properties are investigated. The resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations. Two classes of LPS methods are distinguished: one-level and two-level methods. Numerical examples using bilinear interpolations are presented to validate the analysis and assess the accuracy of both approaches.