A Two-Level Method for Pressure Projection Stabilized P1 Nonconforming Approximation of the Semi-Linear Elliptic Equations (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we study a new stabilized method based on the local pressureprojection to solve the semi-linear elliptic equation. The proposed scheme combinesnonconforming finite element pairs NCP1−P1 triangle element and two-level method,which has a number of attractive computational properties: parameter-free, avoidinghigher-order derivatives or edge-based data structures, but have more favorable stabilityand less support sets. Stability analysis and error estimates have been done. Finally,numerical experiments to check estimates are presented.