Variational solution and error bounds for a nonlinear problem in heat conduction

1971 ◽  
Vol 2 (3) ◽  
pp. 121-125 ◽  
Author(s):  
A. M. Arthurs ◽  
D. Winthrop
Keyword(s):  
Heat Conduction ◽  
Nonlinear Problem ◽  
Error Bounds ◽  
Variational Solution

A Novel Method for Transient Heat Conduction in a Quasi-Periodic Structure With Nonlinear Defects

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Haichao Cui ◽  
Qiang Gao ◽  
Xiaolan Li ◽  
Huajiang Ouyang
Keyword(s):  
Heat Conduction ◽  
Periodic Structure ◽  
Nonlinear Problem ◽  
Superposition Principle ◽  
Nonlinear Problems ◽  
Transient Heat Conduction ◽  
Small Scale ◽  
Novel Method ◽  
Physical Features ◽  
Small Scale Structures

Abstract This paper proposes an efficient numerical method for transient heat conduction in a quasi-periodic structure with nonlinear defects. According to the physical features of transient heat conduction, a quasi-superposition principle for transient heat conduction in a quasi-periodic structure with nonlinear defects is presented, and then a new method is developed to separate the above nonlinear problem to be solved into a linear problem of a perfect periodic structure and nonlinear problems of some small-scale structures with defects. As the scale of nonlinear problem to be solved is significantly reduced and low computational resource is required, outstanding efficiency is achieved. Finally, a numerical example shows that the proposed method is effective and accurate.

Extremum principle for a nonlinear problem in magneto-elasticity

1972 ◽  
Vol 72 (2) ◽  
pp. 315-318 ◽  
Author(s):  
N. Anderson ◽  
A. M. Arthurs ◽  
R. R. Hall
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Problem ◽  
Boundary Value ◽  
Minimum Principle ◽  
Variational Solution ◽  
Extremum Principle ◽  
Integral Inequalities ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Elastic Boundary

AbstractA minimum principle associated with a class of magneto-elastic boundary-value problems is presented. The principle depends on a result on integral inequalities which appears to be new. An accurate variational solution is obtained for an illustrative one-dimensional problem.

Sign in / Sign up

Export Citation Format

Share Document