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A C 0 finite element method for the biharmonic problem without extrinsic penalization
Author(s) -
Gazi Karakoc S. Battal,
Neilan Michael
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.21868
Subject(s) - biharmonic equation , mathematics , extension (predicate logic) , finite element method , hessian matrix , scheme (mathematics) , order (exchange) , mathematical analysis , element (criminal law) , partial differential equation , variety (cybernetics) , pure mathematics , boundary value problem , computer science , physics , statistics , finance , political science , law , economics , thermodynamics , programming language
A symmetric C 0 finite element method for the biharmonic problem is constructed and analyzed. In our approach, we introduce one‐sided discrete second‐order derivatives and Hessian matrices to formulate our scheme. We show that the method is stable and converge with optimal order in a variety of norms. A distinctive feature of the method is that the results hold without extrinsic penalization of the gradient across interelement boundaries. Numerical experiments are given that support the theoretical results, and the extension to Kirchhoff plates is also discussed. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1254–1278, 2014