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A posteriori error estimate for a modified weak Galerkin method solving elliptic problems
Author(s) -
Zhang Tie,
Lin Tao
Publication year - 2017
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.22114
Subject(s) - mathematics , estimator , a priori and a posteriori , galerkin method , residual , discontinuous galerkin method , finite element method , norm (philosophy) , partial differential equation , method of mean weighted residuals , error analysis , mathematical optimization , mathematical analysis , algorithm , statistics , philosophy , physics , epistemology , political science , law , thermodynamics
A residual‐type a posteriori error estimator is proposed and analyzed for a modified weak Galerkin finite element method solving second‐order elliptic problems. This estimator is proven to be both reliable and efficient because it provides computable upper and lower bounds on the actual error in a discrete H 1 ‐norm. Numerical experiments are given to illustrate the effectiveness of the this error estimator. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 381–398, 2017