The Stabilization Of Mixed Finite Element For Second Order Elliptic Problem

In this paper, We present a new stabilized method for the Second order elliptic problem, for the lowest order pairs, they violate the LBB condition. But because they are simple and have a good computational property, they are still a popular choice in practice and the research about their stability is meaningful. First,We get the terms which characterize the LBB'deficiency'of the unstable lowest order spaces. Then, We modify the saddle-point Lagrangian associated with the Second order elliptic problem and get the new stabilized formulation. Compared with the other stabilized methods, they are absolutely stable, need not calculation of higher order derivatives and edge-based data structures, they can achieve optimal accuracy. We present numerical results which show that the new stabilized methods is stable and accurate.