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EXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR SOME SEMILINEAR elliptic equationS IN ANNULUS

Applied Mathematics and Mechanics(English Edition) 2002年第12期23卷 1452-1457页

作者： YAO Qing-liu(姚庆六) MA Qin-sheng(马勤生) Department of Applied Mathematics Nanjing University of EconomicsNanjing 210003 P R China College of Mathematics and Information Science Northwest Normal University Lanzhou 730070 P R China

Applying Krasnosel'skii fixed point theorem of cone expansion-compression type, the existence of positive radial solutions for some second-order nonlinear elliptic equations in annular domains, subject to Dirichlet boundary conditions, is investigated. By considering the properties of nonlinear term on boundary closed intervals, several existence results of positive radial solutions are established. The main results are independent of superlinear growth and sublinear growth of nonlinear term. If nonlinear term has extreme values and satisfies suitable conditions, the main results are very effective.

关键词： second-order elliptic equation annular domain positive radial solution

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Numerical Experiments Using MATLAB: Superconvergence of Nonconforming Finite Element Approximation for second-order elliptic Problems

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Applied Mathematics 2016年第17期7卷 2174-2182页

作者： Anna Harris Stephen Harris Danielle Rauls Department of Mathematics and Computer Science University of Arkansas at Pine Bluff Pine Bluff Arkansas USA US Food and Drug Administration National Center for Toxicology Research Jefferson Arkansas USA

The superconvergence in the finite element method is a phenomenon in which the fi-nite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. However, since the conforming finite element method (CFEM) requires a strong continuity, it is not easy to construct such finite elements for the complex partial differential equations. Thus, the nonconforming finite element method (NCFEM) is more appealing computationally due to better stability and flexibility properties compared to CFEM. The objective of this paper is to establish a general superconvergence result for the nonconforming finite element approximations for second-order elliptic problems by L2-projection methods by applying the idea presented in Wang. MATLAB codes are published at https://***/annaleeharris/Superconvergence-NCFEM for anyone to use and to study. The results of numerical experiments show great promise for the robustness, reliability, flexibility and accuracy of superconvergence in NCFEM by L2- projections.

关键词： Nonconforming Finite Element Methods Superconvergence L2-Projection second-order elliptic equation

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