scholarly journals A New Explicit Formulation by the Finite Element Method and the Finite Difference Method for the Two-Dimensional Convection-Diffusion Equation. Approach by the Error Analysis Techique.

1993 ◽  
Vol 59 (559) ◽  
pp. 833-839
Author(s):  
Yasuhiro Matsuda ◽  
Changcheng Shao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference Method ◽  
Two Dimensional ◽  
Equation Approach ◽  
The Finite Element Method ◽  
Explicit Formulation ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
The Finite Difference Method

Sharpening of metal sheets during electrochemical polishing. Theory and experiments

1984 ◽  
Vol 49 (5) ◽  
pp. 1267-1276
Author(s):  
Petr Novák ◽  
Ivo Roušar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference Method ◽  
The Finite Element Method ◽  
Electrochemical Polishing ◽  
Electrochemical Parameters ◽  
Metal Sheets ◽  
The Finite Difference Method ◽  
Shape Changes ◽  
Theory And Experiments

The electrochemical polishing with simultaneous shape changes of anodes was studied. A theory was derived based on the knowledge of basic electrochemical parameters and the solution of the Laplace equation. To this purpose, the finite element method and the finite difference method with a double transformation of the inter-electrode region were employed. Only the former method proved well and can therefore be recommended for different geometries.

HIGHER-ORDER MASS-LUMPED FINITE ELEMENTS FOR THE WAVE EQUATION

2001 ◽  
Vol 09 (02) ◽  
pp. 671-680 ◽  
Author(s):  
W. A. MULDER
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Wave Equation ◽  
Finite Elements ◽  
Finite Difference Method ◽  
Seismic Wave Propagation ◽  
The Finite Element Method ◽  
Efficient Scheme ◽  
The Finite Difference Method

The finite-element method (FEM) with mass lumping is an efficient scheme for modeling seismic wave propagation in the subsurface, especially in the presence of sharp velocity contrasts and rough topography. A number of numerical simulations for triangles are presented to illustrate the strength of the method. A comparison to the finite-difference method shows that the added complexity of the FEM is amply compensated by its superior accuracy, making the FEM the more efficient approach.

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 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.

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