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A reduced local C 0 discontinuous galerkin method for Kirchhoff plates
Author(s) -
Huang Xuehai,
Huang Jianguo
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.21883
Subject(s) - mathematics , a priori and a posteriori , gaussian , galerkin method , discontinuous galerkin method , space (punctuation) , finite element method , partial derivative , partial differential equation , mathematical analysis , computer science , physics , operating system , thermodynamics , philosophy , epistemology , quantum mechanics
We propose and analyze a reduced local C 0 discontinuous Galerkin (reduced LCDG) method with minimal penalization for Kirchhoff plate bending problems. The resulting linear system of the method can be solved efficiently by Gaussian elimination. Based on the key observation that the reduced LCDG method can be viewed as the localization of Hellan–Herrmann–Johnson method, we are inspired to use the techniques for dealing with the latter method to derive the well‐posedness and a priori error estimates of the reduced LCDG method. With the help of Zienkiewicz–Guzmán–Neilan element space, the a posteriori error analysis is also developed. Some numerical results are provided to demonstrate the theoretical estimates.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1902–1930, 2014