Journal
APPLIED MATHEMATICAL MODELLING
Volume 37, Issue 10-11, Pages 7037-7046Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2013.02.016
Keywords
Two grid method; Stabilized mixed finite element; Semi linear elliptic equations; Inf-sup condition; Pressure projection
Funding
- NSF of China [11271313, 61163027]
- Chinese Ministry of Education [212197]
- China Postdoctoral Science Foundation [201104702, 2012M512056]
- Project of Special Training of the Minority Nationality in Xinjiang [201123117]
- Doctoral Foundation of Xinjiang University [BS110101]
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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. (C) 2013 Elsevier Inc. All rights reserved.
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