scholarly journals Conservación de invariantes de la ecuación de Schrödinger no lineal por el método LDG

2018 ◽  
Vol 64 (1) ◽  
pp. 52 ◽  
Author(s):  
P. E. Castillo ◽  
S. A. Gómez
Keyword(s):  
Finite Element Method ◽  
Discrete Analogue ◽  
Discrete Problem ◽  
The Finite Element Method ◽  
Fully Discrete ◽  
Local Discontinuous Galerkin ◽  
Nonlinear Potentials ◽  
Time Marching ◽  
Theoretical Results ◽  
Marching Scheme

Conservation of the energy and the Hamiltonian of a general non linear Schr¨odinger equation is analyzed for the finite element method “Local Discontinuous Galerkin” spatial discretization. Conservation of the discrete analogue of these quantities is also proved for the fully discrete problem using the modified Crank-Nicolson method as time marching scheme. The theoretical results are validated on a series of problemsfor different nonlinear potentials.

The Convergence of the H-P Version of the Finite Element Method with Quasi-Uniform Meshes for Three Dimensional Poisson Problems with Edge Singularity

2014 ◽  
Vol 644-650 ◽  
pp. 1551-1555
Author(s):  
Jian Ming Zhang ◽  
Yong He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Weighted Sobolev Spaces ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Smooth Functions ◽  
Edge Singularity ◽  
Theoretical Predictions ◽  
Theoretical Results ◽  
Element Method

This paper is concerned with the convergence of the h-p version of the finite element method for three dimensional Poisson problems with edge singularity on quasi-uniform meshes. First, we present the theoretical results for the convergence of the h-p version of the finite element method with quasi-uniform meshes for elliptic problems on polyhedral domains on smooth functions in the framework of Jacobi-weighted Sobolev spaces. Second, we investigate and analyze numerical results for three dimensional Poission problems with edge singularity. Finally, we verified the theoretical predictions by the numerical computation.

Dynamic Analysis and Design of Compliant Mechanisms Using the Finite Element Method

2012 ◽  
Vol 163 ◽  
pp. 111-115 ◽  
Author(s):  
Wen Jing Wang ◽  
Li Ge Zhang ◽  
Shu Sheng Bi
Keyword(s):  
Finite Element Method ◽  
Dynamic Model ◽  
Natural Frequency ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
The Finite Element Method ◽  
Dynamic Effects ◽  
Experiment System ◽  
Analysis And Design ◽  
Theoretical Results

Compliant mechanisms gain at least some of their mobility from the deflection of flexible members rather than from movable joints only. Dynamic effects are very important to improving the design of compliant mechanisms. An investigation on the dynamics and synthesis of the compliant mechanisms is presented. The dynamic model of compliant mechanisms is developed at first. The natural frequency and sensitivity are then studied based on the dynamic model. Finally, optimal design of compliant mechanism is investigated. The experimental study of natural frequency is performed. The comparison between the experiment results and the theoretical results verifies the validity of the experiment system and theoretical model.

scholarly journals Analysis of Vertical Displacements of the Esperanto Footbridge in Bydgoszcz

2018 ◽  
Vol 28 (2) ◽  
pp. 5-17 ◽  
Author(s):  
Adam Bujarkiewicz ◽  
Jarosław Gajewski ◽  
Tomasz Janiak ◽  
Justyna Sobczak-Piąstka ◽  
Jacek Sztubecki ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Simulations ◽  
The Finite Element Method ◽  
Test Load ◽  
Vertical Displacements ◽  
The Subject ◽  
Theoretical Results ◽  
Element Method

Abstract The subject of the research is a footbridge across the river Brda in Bydgoszcz. The measurements of the footbridge displacements with the test load were undertaken. The paper presents the results of the measurements and compares them with the theoretical results obtained using the finite element method (FEM). On this basis, discrepancy between actual work of the structure and numerical simulations was found. Attempt to explain the reasons for the observed differences and direction of further research were included in the conclusions.

A numerical method for two-dimensional nonlinear modified time-fractional fourth-order diffusion equation

2019 ◽  
Vol 10 (01) ◽  
pp. 1941005 ◽  
Author(s):  
Haiyan He ◽  
Kaijie Liang ◽  
Baoli Yin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Fourth Order ◽  
Time Derivative ◽  
Second Order ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Discrete Scheme ◽  
Fully Discrete

In this paper, we consider the finite element method for two-dimensional nonlinear modified time-fractional fourth-order diffusion equation. In order to avoid using higher order elements, we introduce an intermediate variable [Formula: see text] and translate the fourth-order derivative of the original problem into a second-order coupled system. We discretize the fractional time derivative terms by using the [Formula: see text]-approximation and discretize the first-order time derivative term by using the second-order backward differentiation formula. In the fully discrete scheme, we implement the finite element method for the spatial approximation. Unconditional stability of the fully discrete scheme is proven and its optimal convergence order is obtained. Numerical experiments are carried out to demonstrate our theoretical analysis.

scholarly journals The Finite Element Method Applied to a Problem of Blood Flow in Vessels

2012 ◽  
Vol 2012 ◽  
pp. 1-6
Author(s):  
Gabriela Nuţ ◽  
Ioana Chiorean ◽  
Maria Crişan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Blood Flow ◽  
Diffusion Equation ◽  
Discrete Problem ◽  
The Finite Element Method ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
A New Technique ◽  
Element Method

We use the finite element method to solve a convection-diffusion equation when convection is dominating, a problem which describes the behavior of the concentration of a solute in a blood vessel. A new technique for computing the discrete problem is used.

scholarly journals Compressible and nonisothermal viscoelastic flow between eccentrically rotating cylinders

2021 ◽  
Author(s):  
A. T. Mackay ◽  
T. N. Phillips
Keyword(s):  
Unstructured Grid ◽  
Piecewise Linear ◽  
Compressible Fluids ◽  
Discrete Problem ◽  
Rotating Cylinders ◽  
Galerkin Finite Element ◽  
Viscoelastic Parameters ◽  
Time Marching ◽  
The Stability ◽  
Marching Scheme

AbstractA Taylor–Galerkin finite element time marching scheme is derived to numerically simulate the flow of a compressible and nonisothermal viscoelastic liquid between eccentrically rotating cylinders. Numerical approximations to the governing flow and constitutive equations are computed over a custom refined unstructured grid of piecewise linear Galerkin finite elements. An original extension to the DEVSS formulation for compressible fluids is introduced to stabilise solutions of the discrete problem. The predictions of two models: the extended White–Metzner and FENE-P-MP are presented. Comparisons between the torque and load bearing capacity predicted by both models are made over a range of viscoelastic parameters. The results highlight the significant and interacting effects of elasticity and compressibility on journal torque and resultant load, and the stability of the journal bearing system.

Fundamental Solutions of a Normal Force in Semi-Infinite Coating Materials Part I: Solution of Force Acting in the Coating Layer

2011 ◽  
Vol 243-249 ◽  
pp. 5917-5922
Author(s):  
Zhen Yang ◽  
Shi Qun Guo
Keyword(s):  
Finite Element Method ◽  
Normal Force ◽  
Coating Layer ◽  
Recurrence Formula ◽  
Fundamental Solutions ◽  
Image Point ◽  
The Finite Element Method ◽  
Coating Materials ◽  
Order Image ◽  
Theoretical Results

The problem of a normal force acting in the thin layer of semi-infinite coating materials has been studied by adopting the image point technology in this paper. The explicit fundamental solution is given in the series of the displacement functions corresponding to each image point. The displacement functions corresponding to the higher order image points can be determined from those to the lower ones by the recurrence formula presented in this paper. Numerical analysis by means of the finite element method has been carried out to verify the theoretical results. It is found that the accurate enough theoretical solution can be obtained by only taking the displacement functions corresponding to the first several image points into account.

Numerical Modeling of Elastic Modulus and Bucking Load of Honeycombs

2012 ◽  
Vol 271-272 ◽  
pp. 1044-1048
Author(s):  
Ji Ne Li ◽  
Bao Lin Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modeling ◽  
Elastic Modulus ◽  
The Finite Element Method ◽  
Buckling Modes ◽  
Square Cells ◽  
Equivalent Modulus ◽  
Orthotropic Properties ◽  
Theoretical Results

In this paper, both equivalent Young’s modulus and bucking load of the honeycombs are calculated using the finite element method. Honeycombs consisting of either regular hexagonal, equilateral triangular or square cells are considered. Numerical results are systematically compared with theoretical results from other literature. It is found that honeycombs display orthotropic properties. Such a fact is different from that reported in open literature. Moreover, the buckling modes are discussed, and the modified expressions of the equivalent modulus and bucking load are given.

Design Analysis of a Single-Column Pressframe

1984 ◽  
Vol 106 (4) ◽  
pp. 508-516 ◽  
Author(s):  
U. P. Singh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Curved Beam ◽  
Thin Wall ◽  
The Finite Element Method ◽  
Beam Elements ◽  
Single Column ◽  
Deformed State ◽  
Strength And Stiffness ◽  
Theoretical Results

It is observed in practice that the classic (conventional) method as well as the finite element method, when using beam elements, to evaluate the strength and stiffness of a pressframe, gives results differing substantially from actual values. This discrepancy between experimental and theoretical results can be considerably narrowed if the stress-deformed state of the corner zone is separately considered in the computation of the overall strength and stiffness of the pressframe. By means of the application of the theory of thin-wall curved beam with large curvature it is economically possible to analyze the stress-deformed behavior of the pressform in general and the corner zone element in particular with fair reliability. In the present paper this method is applied to a mechanical C-frame press.

Development of a wheel mounted disc brake for a high-speed train

1998 ◽  
Vol 212 (2) ◽  
pp. 113-121 ◽  
Author(s):  
M Tirovic
Keyword(s):  
Finite Element Method ◽  
Thermal Effects ◽  
High Speed ◽  
Development Time ◽  
Disc Brake ◽  
High Speed Train ◽  
The Finite Element Method ◽  
Detailed Design ◽  
Successful Design ◽  
Theoretical Results

This paper describes the development of a wheel mounted disc brake for the power car of a high-speed train. The disc design consists of two rings bolted on to the wheel hub, one either side of the wheel. The finite element method was used extensively from the very beginning of the design process. This considerably reduced development time and enabled the successful design of a disc for an extremely severe duty. Modelling of bulk thermal effects was found to be most effective for shape optimization and prediction of global disc behaviour, with more sophisticated analyses required to determine more detailed design limits. Results from dynamometer tests and vehicle trials gave good correlation with theoretical results and proved the design suitability for the required duty.

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