Application of the finite‐element method and the finite‐difference method to photothermal inspections

1996 ◽  
Vol 79 (12) ◽  
pp. 9084-9089 ◽  
Author(s):  
G. Goch ◽  
M. Reigl
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
The Finite Element Method ◽  
The Finite Difference Method ◽  
Element Method

scholarly journals The optimal dimensions of the domain for solving the single-band Schrödinger equation by the finite-difference and finite-element methods

2014 ◽  
Vol 11 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Dusan Topalovic ◽  
Stefan Pavlovic ◽  
Nemanja Cukaric ◽  
Milan Tadic
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Finite Element Methods ◽  
Ground State ◽  
Difference Method ◽  
Grid Size ◽  
The Finite Element Method ◽  
The Finite Difference Method

The finite-difference and finite-element methods are employed to solve the one-dimensional single-band Schr?dinger equation in the planar and cylindrical geometries. The analyzed geometries correspond to semiconductor quantum wells and cylindrical quantum wires. As a typical example, the GaAs/AlGaAs system is considered. The approximation of the lowest order is employed in the finite-difference method and linear shape functions are employed in the finite-element calculations. Deviations of the computed ground state electron energy in a rectangular quantum well of finite depth, and for the linear harmonic oscillator are determined as function of the grid size. For the planar geometry, the modified P?schl-Teller potential is also considered. Even for small grids, having more than 20 points, the finite-element method is found to offer better accuracy than the finite-difference method. Furthermore, the energy levels are found to converge faster towards the accurate value when the finite-element method is employed for calculation. The optimal dimensions of the domain employed for solving the Schr?dinger equation are determined as they vary with the grid size and the ground-state energy.

Finite-Difference Method Appliance to the Computation of Ground Additional Stress and Settlement of Storage Tank

2011 ◽  
Vol 243-249 ◽  
pp. 2638-2642
Author(s):  
Xu Dong Cheng ◽  
Wen Shan Peng ◽  
Lei Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Storage Tank ◽  
Three Dimensional ◽  
Additional Stress ◽  
The Finite Element Method ◽  
The Finite Difference Method

This paper adopts the Finite-difference method to research the distribution of ground additional stress and distortion in differently isotropic and non-isotropic foundation conditions, and uses the Finite-difference method to compare with the Finite-element method and the three-dimensional settlement method used by the code. Through comparative analysis, the reliability and superiority of Finite-difference method used for calculating ground additional stress and settlement are justified.

scholarly journals The finite difference versus the finite element method for the solution of boundary value problems

1984 ◽  
Vol 29 (2) ◽  
pp. 267-288
Author(s):  
Vidar Thomée
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
The Finite Element Method ◽  
Discretization Schemes ◽  
The Finite Difference Method ◽  
Element Method

In this lecture we describe, discuss and compare the two classes of methods most commonly used for the numerical solution of boundary value problems for partial differential equations, namely, the finite difference method and the finite element method. For both of these methods an extensive development of mathematical error analysis has taken place but individual numerical analysts often express strong prejudices in favor of one of them. Our purpose is to try to convey our conviction that this attitude is both historically unjustified and inhibiting, and that familiarity with both methods provides a wider range of techniques for constructing and analyzing discretization schemes.

Study and Simulate the Air Pollution Based on the Finite Difference Method

2012 ◽  
Vol 518-523 ◽  
pp. 2820-2824
Author(s):  
Yi Ni Guo ◽  
Yan Zhang ◽  
Jian Wang ◽  
Ye Huang
Keyword(s):  
Finite Element Method ◽  
Air Pollution ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
The Finite Element Method ◽  
Liquid Diffusion ◽  
Continuous Problems ◽  
The Finite Difference Method ◽  
The Difference

The finite difference method that is the finite element method is used to solve the plane continuous problems. In this article, the theory and method of the finite difference method, as well as the application on the boundary problem are introduced. By analyzing the potential flew field equation and liquid diffusion equation, they are discreted using the difference method and the numerical analysis under certain boundary condition is conducted. In air pollution, the smoke in the diffusion is typical planar continuous problems. In this paper, the finite difference method is used to analyse and simulate the spread of the smoke.

GALERKIN FINITE ELEMENT METHOD AND FINITE DIFFERENCE METHOD FOR SOLVING CONVECTIVE NON-LINEAR EQUATION

2010 ◽  
Vol 9 (1-2) ◽  
pp. 69
Author(s):  
E. C. Romão ◽  
M. D. De Campos ◽  
L. F. M. De Moura
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Convection Diffusion ◽  
Non Linear ◽  
Element Method

The fast progress has been observed in the development of numerical and analytical techniques for solving convection-diffusion and fluid mechanics problems. Here, a numerical approach, based in Galerkin Finite Element Method with Finite Difference Method is presented for the solution of a class of non-linear transient convection-diffusion problems. Using the analytical solutions and the L2 and L∞ error norms, some applications is carried and valuated with the literature.

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