A two-grid stabilized mixed finite element method for semilinear elliptic equations

作者：Weng Zhifeng; Feng Xinlong^*; Liu Demin

来源：Applied Mathematical Modelling, 2013, 37(10-11): 7037-7046.

DOI：10.1016/j.apm.2013.02.016

• Two grid method
• Stabilized mixed finite element
• Semi linear elliptic equations
• Inf-sup condition
• Pressure projection

In this paper, we present a two-grid stabilized mixed finite element method for the two-dimensional semilinear elliptic equations. The method combines the two grid scheme with a stabilized mixed finite element method which is based on pressure projection stabilization method by using the lowest equal-order pair for the velocity and pressure. The two-grid method consists of solving a small semilinear system on the coarse mesh and then solving a linear system on the fine mesh. It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy H = O(h(1/2)). Error estimates are derived for the algorithm of the two-grid method. Finally, we give some numerical experiments to verify the efficiency and the theoretical results of the proposed method.

• 出版日期2013-6-1
• 单位武汉大学; 新疆大学