A C0 finite element method for the biharmonic problem without extrinsic penalization. Issue 4 (4th March 2014)

• Record Type: Journal Article
• Authors: Gazi Karakoc, S. Battal; Neilan, Michael
• Is Part Of: Numerical methods for partial differential equations. Volume 30:Issue 4(2014:Jul.)
• Page Start: 1254
• Page End: 1278
• Publication Date: 2014-03-04
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21868
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>A symmetric <italic>C</italic>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</p> </abstract>