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A compact C 0 discontinuous Galerkin method for Kirchhoff plates
Author(s) -
An Rong,
Huang Xuehai
Publication year - 2015
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.21946
Subject(s) - mathematics , stencil , finite element method , norm (philosophy) , stiffness matrix , mathematical analysis , a priori and a posteriori , discontinuous galerkin method , galerkin method , differential operator , operator (biology) , sobolev space , physics , philosophy , biochemistry , chemistry , computational science , epistemology , repressor , political science , transcription factor , gene , law , thermodynamics
A compact C 0 discontinuous Galerkin (CCDG) method is developed for solving the Kirchhoff plate bending problems. Based on the CDG (LCDG) method for Kirchhoff plate bending problems, the CCDG method is obtained by canceling the term of global lifting operator and enhancing the term of local lifting operator. The resulted CCDG method possesses the compact stencil, that is only the degrees of freedom belonging to neighboring elements are connected. The advantages of CCDG method are: (1) CCDG method just requires C 0 finite element spaces; (2) the stiffness matrix is sparser than CDG (LCDG) method; and (3) it does not contain any parameter which can not be quantified a priori compared to C 0 interior penalty (IP) method. The optimal order error estimates in certain broken energy norm and H 1 ‐norm for the CCDG method are derived under minimal regularity assumptions on the exact solution with the help of some local lower bound estimates of a posteriori error analysis. Some numerical results are included to verify the theoretical convergence orders. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1265–1287, 2015