A posteriori error estimates of edge residual type of finite element method for nonmonotone quasi‐linear elliptic problems | Zendy

Guo Liming | Zendy; Huang Ziping | Zendy; Wang Cheng | Zendy

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A posteriori error estimates of edge residual type of finite element method for nonmonotone quasi‐linear elliptic problems

Author(s) -

Guo Liming,

Huang Ziping,

Wang Cheng

Publication year - 2014

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.21838

Subject(s) - estimator , mathematics , a priori and a posteriori , residual , finite element method , norm (philosophy) , enhanced data rates for gsm evolution , method of mean weighted residuals , partial differential equation , mathematical optimization , mathematical analysis , algorithm , statistics , computer science , telecommunications , philosophy , physics , epistemology , galerkin method , political science , law , thermodynamics

In this article, we study the edge residual‐based a posteriori error estimates of conforming linear finite element method for nonmonotone quasi‐linear elliptic problems. It is proven that edge residuals dominate a posteriori error estimates. Up to higher order perturbations, edge residuals can act as a posteriori error estimators. The global reliability and local efficiency bounds are established both in H 1 ‐norm and L 2 ‐norm. Numerical experiments are provided to illustrate the performance of the proposed error estimators. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 813–837, 2014

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