A New Finite Element Gradient Recovery Method: Superconvergence Property

2005 ◽  
Vol 26 (4) ◽  
pp. 1192-1213 ◽  
Author(s):  
Zhimin Zhang ◽  
Ahmed Naga
Keyword(s):  
Finite Element ◽  
Gradient Recovery ◽  
Recovery Method

scholarly journals Finite Element Model for Linear Elastic Thick Shells Using Gradient Recovery Method

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Achille Germain Feumo ◽  
Robert Nzengwa ◽  
Joseph Nkongho Anyi
Keyword(s):  
Finite Element ◽  
Fundamental Form ◽  
Element Model ◽  
Shear Stresses ◽  
Gradient Recovery ◽  
Recovery Method ◽  
The Third ◽  
New Family ◽  
Convergence Results ◽  
Third Fundamental Form

This research purposed a new family of finite elements for spherical thick shell based on Nzengwa-Tagne’s model proposed in 1999. The model referred to hereafter as N-T model contains the classical Kirchhoff-Love (K-L) kinematic with additional terms related to the third fundamental form governing strain energy. Transverse shear stresses are computed and C0 finite element is proposed for numerical implementation. However, using straight line triangular elements does not guarantee a correct computation of stress across common edges of adjacent elements because of gradient jumps. The gradient recovery method known as Polynomial Preserving Recovery (PPR) is used for local interpolation and applied on a hemisphere under diametrically opposite charges. A good agreement of convergence results is observed; numerical results are compared to other results obtained with the classical K-L thin shell theory. Moreover, simulation on increasing values of the ratio of the shell shows impact of the N-T model especially on transverse stresses because of the significant energy contribution due to the third fundamental form tensor present in the kinematics of this model. The analysis of the thickness ratio shows difference between the classical K-L theory and N-T model when the ratio is greater than 0.099.

Superconvergence Analysis of Gradient Recovery Method for TM Model of Electromagnetic Scattering in the Cavity

2017 ◽  
Vol 9 (5) ◽  
pp. 1133-1144
Author(s):  
Shanghui Jia ◽  
Changhui Yao
Keyword(s):  
Finite Element ◽  
Electromagnetic Scattering ◽  
Gradient Recovery ◽  
Recovery Method ◽  
Face Type ◽  
Numerical Example ◽  
Polynomial Preserving ◽  
Recovery Technique ◽  
Tm Model

AbstractIn this paper, we consider the transform magnetic (TM) model of electromagnetic scattering in the cavity. By the Polynomial Preserving Recovery technique, we present superconvergence analysis for the vertex-edge-face type finite element. From the numerical example, we can see that the provided method is efficient and stable.

Superconvergence Analysis of Gradient Recovery Method for TM Model of Electromagnetic Scattering in the Cavity

2017 ◽  
Vol 9 (3) ◽  
pp. 543-553 ◽  
Author(s):  
Shanghui Jia ◽  
Changhui Yao ◽  
Hehu Xie
Keyword(s):  
Finite Element ◽  
Electromagnetic Scattering ◽  
Gradient Recovery ◽  
Recovery Method ◽  
Face Type ◽  
Numerical Example ◽  
Polynomial Preserving ◽  
Recovery Technique ◽  
Tm Model

AbstractIn this paper, we consider the transform magnetic (TM) model of electromagnetic scattering in the cavity. By the Polynomial Preserving Recovery technique, we present superconvergence analysis for the vertex-edge-face type finite element. From the numerical example, we can see that the provided method is efficient and stable.

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.

Sign in / Sign up

Export Citation Format

Share Document