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 High-accuracy analysis of finite-element method for two-term mixed time-fractional diffusion-wave equations

2018 ◽  
Vol 48 (7) ◽  
pp. 871-887 ◽  
Author(s):  
Yabing WEI ◽  
Yanmin ZHAO ◽  
Yifa TANG ◽  
Fenling WANG ◽  
Zhengguang SHI ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Equations ◽  
Fractional Diffusion ◽  
High Accuracy ◽  
Accuracy Analysis ◽  
Diffusion Wave ◽  
Element Method

Seismic Stability Analysis of Light-Weight Column Considering Depth of Liquefiable Layer

2014 ◽  
Vol 638-640 ◽  
pp. 1956-1960
Author(s):  
Bin Bin Xu ◽  
Kentaro Nakai ◽  
Toshihiro Noda
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stability Analysis ◽  
Ground Surface ◽  
High Accuracy ◽  
Seismic Stability ◽  
Embedment Depth ◽  
Light Weight ◽  
Accuracy Analysis ◽  
Gas Supply

A series of light-weight column for receiving the wireless signals to control the stoppage of gas supply are built on the liquefiable ground and their seismic stability should be precisely investigated to prevent the second accident. For the conventional judgment of liquefiable ground, if the soil type of the ground surface is the same, the potential liquefaction of the ground is also the same. In this paper, based on the soil-water coupled finite element method the influence of the depth of the liquefiable layer is taken into consideration and it is found that the seismic stability of the column varies significantly depending on the depth of liquefiable layer even though the embedment depth of the column is the same. Therefore, it is necessary to con-sider the depth of liquefiable layer for the high accuracy analysis.

scholarly journals High Accuracy Analysis of Nonconforming Mixed Finite Element Method for the Nonlinear Sivashinsky Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Lele Wang ◽  
Xin Liao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
Special Property ◽  
Mixed Finite Element Method ◽  
High Accuracy ◽  
Accuracy Analysis ◽  
Interpolation Postprocessing ◽  
Sivashinsky Equation ◽  
Element Method

The fourth-order nonlinear Sivashinsky equation is often used to simulate a planar solid-liquid interface for a binary alloy. In this paper, we study the high accuracy analysis of the nonconforming mixed finite element method (MFEM for short) for this equation. Firstly, by use of the special property of the nonconforming EQ1rot element (see Lemma 1), the superclose estimates of order Oh2+Δt in the broken H1-norm for the original variable u and intermediate variable p are deduced for the back-Euler (B-E for short) fully-discrete scheme. Secondly, the global superconvergence results of order Oh2+Δt for the two variables are derived through interpolation postprocessing technique. Finally, a numerical example is provided to illustrate validity and efficiency of our theoretical analysis and method.

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.

Superconvergence Analysis of Finite Element Method for Onlinear Klein-Gordon Equation

2014 ◽  
Vol 527 ◽  
pp. 343-346
Author(s):  
Yu Shi ◽  
Hong Ling Meng ◽  
Qian Jia ◽  
Dong Yang Shi
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Gordon Equation ◽  
High Accuracy ◽  
Accuracy Analysis ◽  
Element Analysis ◽  
Klein Gordon ◽  
Indispensable Tool ◽  
Klein Gordon Equation

The standard finite elements of degree p over the rectangular meshes are applied to a non-linear Klein-Gordon equation. By utilizing the properties of interpolation on the element, high accuracy analysis and derivative delivery techniques with respect to time t instead of the traditional Ritz projection operator, which is an indispensable tool in the traditional finite element analysis, the supercloseproperty with order is obtained. Furthermore, the superconvergence result is derived through the postprocessing approach.

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