scholarly journals Polynomial preserving recovery on boundary

2016 ◽  
Vol 307 ◽  
pp. 119-133 ◽  
Author(s):  
Hailong Guo ◽  
Zhimin Zhang ◽  
Ren Zhao ◽  
Qingsong Zou
Keyword(s):  
Polynomial Preserving

Polynomial preserving virtual elements with curved edges

2020 ◽  
Vol 30 (08) ◽  
pp. 1555-1590 ◽  
Author(s):  
L. Beirão da Veiga ◽  
F. Brezzi ◽  
L. D. Marini ◽  
A. Russo
Keyword(s):  
Theoretical Analysis ◽  
Patch Test ◽  
Small Scale ◽  
Intermediate Scale ◽  
Numerical Tests ◽  
Polynomial Preserving ◽  
Virtual Element

In this paper, we tackle the problem of constructing conforming Virtual Element spaces on polygons with curved edges. Unlike previous VEM approaches for curvilinear elements, the present construction ensures that the local VEM spaces contain all the polynomials of a given degree, thus providing the full satisfaction of the patch test. Moreover, unlike standard isoparametric FEM, this approach allows to deal with curved edges at an intermediate scale, between the small scale (treatable by homogenization) and the bigger one (where a finer mesh would make the curve flatter and flatter). The proposed method is supported by theoretical analysis and numerical tests.

A Type of Finite Element Gradient Recovery Method based on Vertex-Edge-Face Interpolation: The Recovery Technique and Superconvergence Property

2011 ◽  
Vol 1 (3) ◽  
pp. 248-263
Author(s):  
Qun Lin ◽  
Hehu Xie
Keyword(s):  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
A Posteriori ◽  
Gradient Recovery ◽  
Recovery Method ◽  
A Posteriori Error ◽  
Numerical Examples ◽  
Polynomial Preserving ◽  
New Type ◽  
Recovery Technique

AbstractIn this paper, a new type of gradient recovery method based on vertex-edge-face interpolation is introduced and analyzed. This method gives a new way to recover gradient approximations and has the same simplicity, efficiency, and superconvergence properties as those of superconvergence patch recovery method and polynomial preserving recovery method. Here, we introduce the recovery technique and analyze its superconvergence properties. We also show a simple application in the a posteriori error estimates. Some numerical examples illustrate the effectiveness of this recovery method.

scholarly journals New polynomial preserving operators on simplices: direct results

2004 ◽  
Vol 131 (1) ◽  
pp. 59-73 ◽  
Author(s):  
Elena Berdysheva ◽  
Kurt Jetter ◽  
Joachim Stöckler
Keyword(s):  
Polynomial Preserving ◽  
Direct Results
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