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A Two-Level Method for Pressure Projection Stabilized P1 Nonconforming Approximation of the Semi-Linear Elliptic Equations

Part of: Numerical methods Equations of mathematical physics and other areas of application Partial differential equations, boundary value problems

Published online by Cambridge University Press:  27 January 2016

Sufang Zhang ,
Hongxia Yan  and
Hongen Jia
Sufang Zhang
Affiliation:
College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
Hongxia Yan
Affiliation:
Department of Science and Technology, China University of Political Science and Law, Beijing 102249, China
Hongen Jia*
Affiliation:
College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
*
*Corresponding author. Email: zsfczg@163.com (S. Zhang), yhxch@vip.sina.com (H. Yan), jiahongen@aliyun.com (H. Jia)
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Abstract.

In this paper, we study a new stabilized method based on the local pressure projection to solve the semi-linear elliptic equation. The proposed scheme combines nonconforming finite element pairs NCP1–P1 triangle element and two-level method, which has a number of attractive computational properties: parameter-free, avoiding higher-order derivatives or edge-based data structures, but have more favorable stability and less support sets. Stability analysis and error estimates have been done. Finally, numerical experiments to check estimates are presented.

Keywords

Semi-linear elliptic equationstwo-level methodnonconforming finite element methodstabilized method

MSC classification

Secondary: 35Q30: Navier-Stokes equations 74S05: Finite element methods 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 3 , June 2016 , pp. 386 - 398
Copyright
Copyright © Global-Science Press 2016 

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