STABILITY ANALYSIS FOR THE ENERGY PRESERVING FINITE DIFFERENCE SCHEME FOR ALLEN-CAHN EQUATION AND SOME REMARKS ON THE RELATIONSHIP OF THE ENERGY PRESERVING FINITE DIFFERENCE SCHEME AND FINITE ELEMENT SCHEME

2017 ◽  
Vol 16 (2) ◽  
pp. 95-106
Author(s):  
Takanori Ide
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Cahn Equation ◽  
Relationship Of ◽  
The Relationship

Analyses of the Dispersion Overshoot and Inverse Dissipation of the High-Order Finite Difference Scheme

2013 ◽  
Vol 5 (06) ◽  
pp. 809-824 ◽  
Author(s):  
Qin Li ◽  
Qilong Guo ◽  
Hanxin Zhang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
High Order ◽  
Staggered Grid ◽  
Third Order ◽  
Order Scheme ◽  
Relationship Of ◽  
High Order Finite Difference ◽  
The Relationship

AbstractAnalyses were performed on the dispersion overshoot and inverse dissipation of the high-order finite difference scheme using Fourier and precision analysis. Schemes under discussion included the pointwise- and staggered-grid type, and were presented in weighted form using candidate schemes with third-order accuracy and three-point stencil. All of these were commonly used in the construction of difference schemes. Criteria for the dispersion overshoot were presented and their critical states were discussed. Two kinds of instabilities were studied due to inverse dissipation, especially those that occur at lower wave numbers. Criteria for the occurrence were presented and the relationship of the two instabilities was discussed. Comparisons were made between the analytical results and the dispersion/dissipation relations by Fourier transformation of typical schemes. As an example, an application of the criteria was given for the remedy of inverse dissipation in Weirs & Martín’s third-order scheme.

scholarly journals Supraconvergence of a Finite Difference Scheme for Elliptic Boundary Value Problems of the Third Kind in Fractional Order Sobolev Spaces

2006 ◽  
Vol 6 (2) ◽  
pp. 154-177 ◽  
Author(s):  
E. Emmrich ◽  
R.D. Grigorieff
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Elliptic Boundary ◽  
Special Kind ◽  
Variable Coefficients ◽  
Second Order ◽  
Nonuniform Grids ◽  
Close Relationship

AbstractIn this paper, we study the convergence of the finite difference discretization of a second order elliptic equation with variable coefficients subject to general boundary conditions. We prove that the scheme exhibits the phenomenon of supraconvergence on nonuniform grids, i.e., although the truncation error is in general of the first order alone, one has second order convergence. All error estimates are strictly local. Another result of the paper is a close relationship between finite difference scheme and linear finite element methods combined with a special kind of quadrature. As a consequence, the results of the paper can be viewed as the introduction of a fully discrete finite element method for which the gradient is superclose. A numerical example is given.

A stability analysis for a generalized finite-difference scheme applied to the pure advection equation

2018 ◽  
Vol 147 ◽  
pp. 293-300 ◽  
Author(s):  
G. Tinoco-Guerrero ◽  
F.J. Domínguez-Mota ◽  
A. Gaona-Arias ◽  
M.L. Ruiz-Zavala ◽  
J.G. Tinoco-Ruiz
Keyword(s):  
Stability Analysis ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Advection Equation
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