期刊
JOURNAL OF SCIENTIFIC COMPUTING
卷 52, 期 3, 页码 519-545出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-011-9557-4
关键词
Semilinear elliptic equations; Finite volume methods; P-1-nonconforming quadrilateral element; Q(1)-conforming quadrilateral element; Superconvergence
资金
- National Natural Science Foundation of China [10971166, 10901131, 61163027]
- National High Technology Research and Development Program of China (863 Program) [2009AA01A135]
- China Postdoctoral Science Foundation [201104702, 200801448]
- Natural Science Foundation of Xinjiang Province [2010211B04]
In this paper we use P (1)-nonconforming quadrilateral finite volume methods with interpolated coefficients to solve the semilinear elliptic problems. Two types of control volumes are applied. Optimal error estimates in H (1)-norm on the quadrilateral mesh and superconvergence of derivative on the rectangular mesh are derived by using the continuity argument, respectively. In addition, numerical experiments are presented adequately to confirm the theoretical analysis and optimal error estimates in L (2)-norm is also observed obviously. Compared with the standard Q (1)-conforming quadrilateral element, numerical results of the proposed finite volume methods show its better performance than others.
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