scholarly journals Superconvergence Analysis of Finite Element Method for a Second-Type Variational Inequality

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Dongyang Shi ◽  
Hongbo Guan ◽  
Xiaofei Guan
Keyword(s):  
Finite Element Method ◽  
Exact Solution ◽  
Finite Element ◽  
Variational Inequality ◽  
Theoretical Analysis ◽  
Error Estimate ◽  
Numerical Results ◽  
Previous Literature ◽  
Superconvergence Results ◽  
Norm Error

This paper studies the finite element (FE) approximation to a second-type variational inequality. The supe rclose and superconvergence results are obtained for conforming bilinear FE and nonconformingEQrotFE schemes under a reasonable regularity of the exact solutionu∈H5/2(Ω), which seem to be never discovered in the previous literature. The optimalL2-norm error estimate is also derived forEQrotFE. At last, some numerical results are provided to verify the theoretical analysis.

Finite Element Analysis to a Kind of Elliptic Variational Inequality

2012 ◽  
Vol 557-559 ◽  
pp. 2126-2129
Author(s):  
Jun Hui Zhu ◽  
Chun Rui Cheng ◽  
Guang Pu Lou
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Variational Inequality ◽  
Error Estimate ◽  
Finite Element Methods ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Nonlinear Materials ◽  
Elliptic Variational Inequality

Finite element methods for the elliptic variational inequality of the second kind deduced from friction problems or nonlinear materials in elasticity have been discussed. In this paper, the finite element method with numerical integration for the second type elliptic variational inequality is considered and an error estimate is proved.

scholarly journals New High Accuracy Analysis of a Double Set Parameter Nonconforming Element for the Clamped Kirchhoff Plate Unilaterally Constrained by an Elastic Obstacle

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2038
Author(s):  
Dongyang Shi ◽  
Lifang Pei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Theoretical Analysis ◽  
Error Estimate ◽  
High Accuracy ◽  
Kirchhoff Plate ◽  
Interpolation Operator ◽  
Accuracy Analysis ◽  
Nonconforming Element ◽  
Novel Approaches

In this paper, a non-C0 double set parameter finite element method is presented for the clamped Kirchhoff plate with an elastic unilateral obstacle. A new high accuracy error estimate with order O(h2) in the broken energy norm is derived by use of a series of novel approaches, including some special features of the element and an incomplete biquadratic interpolation operator. At the same time, some experimental results are provided to verify the theoretical analysis.

scholarly journals Superconvergence of a finite element method for linear integro-differential problems

2000 ◽  
Vol 23 (5) ◽  
pp. 343-359 ◽  
Author(s):  
Do Y. Kwak ◽  
Sungyun Lee ◽  
Qian Li
Keyword(s):  
Finite Element Method ◽  
Exact Solution ◽  
Finite Element ◽  
Approximate Solution ◽  
Second Order ◽  
Initial Condition ◽  
First Order ◽  
Superconvergence Results ◽  
Global Superconvergence ◽  
Element Method

We introduce a new way of approximating initial condition to the semidiscrete finite element method for integro-differential equations using any degree of elements. We obtain several superconvergence results for the error between the approximate solution and the Ritz-Volterra projection of the exact solution. Fork>1, we obtain first order gain inLp(2≤p≤∞)norm, second order inW1,p(2≤p≤∞)norm and almost second order inW1,∞norm. Fork=1, we obtain first order gain inW1,p(2≤p≤∞)norms. Further, applying interpolated postprocessing technique to the approximate solution, we get one order global superconvergence between the exact solution and the interpolation of the approximate solution in theLpandW1,p(2≤p≤∞).

A Numerical Analysis for Cracks Emanating from a Quarter-Spherical Cavity on the Edge of an Elastic Body

2012 ◽  
Vol 499 ◽  
pp. 243-247
Author(s):  
Long Hai Yan ◽  
Bao Liang Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Elastic Body ◽  
Spherical Cavity ◽  
Numerical Results ◽  
Shielding Effect ◽  
Corner Crack ◽  
Element Method

This note is specifically concerned with cracks emanating from a quarter-spherical cavity on the edge in an elastic body (see Fig.1) by using finite element method. The numerical results show that the existence of the cavity has a shielding effect of the corner crack. In addition, it is found that the effect of boundaries parallel to the crack on the SIFs is obvious when.H/R≤3

scholarly journals Evaluation of Pile’s Buckling Under Axial Load by B-Spline Method and Comparison With Finite Element Method and Exact Solution

2018 ◽  
Vol 8 (2) ◽  
pp. 29-34
Author(s):  
A. Moghaddam ◽  
A. Nayeri ◽  
S.M. Mirhosseini
Keyword(s):  
Finite Element Method ◽  
Exact Solution ◽  
Finite Element ◽  
Numerical Methods ◽  
High Volume ◽  
Spline Method ◽  
B Spline ◽  
Volume Calculations ◽  
Reaction Coefficient ◽  
Element Method

Abstract Although various analytical and numerical methods have been proposed by researchers to solve equations, but use of numerical tools with low volume calculations and high accuracy instead of other numerical methods with high volume calculations is inevitable in the analysis of engineering equations. In this paper, B-Spline spectral method was used to study buckling equations of the piles. Results were compared with the calculated amounts of the exact solution and finite element method. Uniform horizontal reaction coefficient has been used in most of proposed methods for analyzing buckling of the pile on elastic base. In reality, soil horizontal reaction coefficient is nonlinear along the pile. So, in this research by using B-Spline method, buckling equation of the pile with nonlinear horizontal reaction coefficient of the soil was investigated. It is worth mentioning that B-Spline method had not been used for buckling of the pile.

The Semi-Discrete Finite Element Method for the Cauchy Equation

2014 ◽  
Vol 668-669 ◽  
pp. 1130-1133
Author(s):  
Lei Hou ◽  
Xian Yan Sun ◽  
Lin Qiu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Results ◽  
Cauchy Equation ◽  
The Time Domain ◽  
Nicolson Scheme ◽  
Discrete Finite Element ◽  
Better Than ◽  
Element Method ◽  
Crank Nicolson

In this paper, we employ semi-discrete finite element method to study the convergence of the Cauchy equation. The convergent order can reach. In numerical results, the space domain is discrete by Lagrange interpolation function with 9-point biquadrate element. The time domain is discrete by two difference schemes: Euler and Crank-Nicolson scheme. Numerical results show that the convergence of Crank-Nicolson scheme is better than that of Euler scheme.

Computer-Aided Modelling of Cloth Deformation

1996 ◽  
Author(s):  
Y. F. Zhao ◽  
S. T. Tan ◽  
T. N. Wong ◽  
W. J. Chen
Keyword(s):  
Finite Element Method ◽  
Exact Solution ◽  
Finite Element ◽  
Rigid Body ◽  
Present Method ◽  
Geometric Constraint ◽  
Computationally Efficient ◽  
Large Rotation ◽  
Developable Surfaces ◽  
Computer Aided

Abstract A constrained finite element method for modelling cloth deformation is developed. The bending deformation and the geometric constraint of developable surfaces of the cloth objects are considered. The representation of large rotation and the motion of rigid body are described using the current coordinates with the geometric constraint. The effectiveness of the present method is verified by comparing the thread deformation with the exact solution of catenary. Several examples are given to show that the proposed method converges quickly and is thus computationally efficient.

Sign in / Sign up

Export Citation Format

Share Document