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|Title:||On the Poincaré-Friedrichs inequality for piecewise H1 functions in anisotropic discontinuous Galerkin finite element methods|
Crouzeix-Raviart nonconforming linear element
Discontinuous galerkin finite element method
Poincaré-Friedrichs inequality of piecewise H1 function
The maximum angle condition
|Citation:||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|
|Appears in Collections:||Staff Publications|
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