Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/103826
Title: On the Poincaré-Friedrichs inequality for piecewise H1 functions in anisotropic discontinuous Galerkin finite element methods
Authors: Duan, H.-Y.
Tan, R.C.E. 
Keywords: Anisotropic mesh
Crouzeix-Raviart nonconforming linear element
Discontinuous galerkin finite element method
Poincaré-Friedrichs inequality of piecewise H1 function
Shape-regular condition
The maximum angle condition
Issue Date: 2010
Source: Duan, H.-Y.,Tan, R.C.E. (2010). On the Poincaré-Friedrichs inequality for piecewise H1 functions in anisotropic discontinuous Galerkin finite element methods. Mathematics of Computation 80 (273) : 119-140. ScholarBank@NUS Repository.
Abstract: The purpose of this paper is to propose a proof for the Poincaré-Friedrichs inequality for piecewise H1 functions on anisotropic meshes. By verifying suitable assumptions involved in the newly proposed proof, we show that the Poincaré-Friedrichs inequality for piecewise H1 functions holds independently of the aspect ratio which characterizes the shape-regular condition in finite element analysis. In addition, under the maximum angle condition, we establish the Poincaré-Friedrichs inequality for the Crouzeix-Raviart nonconforming linear finite element. Counterexamples show that the maximum angle condition is only sufficient. © 2010 American Mathematical Society.
Source Title: Mathematics of Computation
URI: http://scholarbank.nus.edu.sg/handle/10635/103826
ISSN: 00255718
Appears in Collections:Staff Publications

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