Integration of a Linear Parabolic Equation

2002 ◽  
pp. 53-62
Author(s):  
Jean-Jacques Chattot
Keyword(s):  
Parabolic Equation ◽  
Linear Parabolic Equation

Time and space meshes adaptivity for the resolution of a semi-linear heat equation

2021 ◽  
pp. 1-10
Author(s):  
Nejmeddine Chorfi
Keyword(s):  
Parabolic Equation ◽  
Heat Equation ◽  
Order Of Convergence ◽  
Linear Parabolic Equation ◽  
Spectral Elements ◽  
Euler Scheme ◽  
Time Step ◽  
Implicit Euler Scheme ◽  
Linear Heat ◽  
Error Indicators

The aim of this work is to highlight that the adaptivity of the time step when combined with the adaptivity of the spectral mesh is optimal for a semi-linear parabolic equation discretized by an implicit Euler scheme in time and spectral elements method in space. The numerical results confirm the optimality of the order of convergence. The later is similar to the order of the error indicators.

Controllability Property of a Superlinear Climate System

2013 ◽  
Vol 367 ◽  
pp. 264-269
Author(s):  
Liang Zhang ◽  
Yang Liu
Keyword(s):  
Fixed Point ◽  
Parabolic Equation ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Point Of View ◽  
Climate System ◽  
Linear Parabolic Equation ◽  
Controllability Property

This work concerns a climate system in the point of view of controllability. We obtain by the Kakutani’s fixed point theorem and the controllability property of the linear parabolic equation that the superlinear climate system is null controllable in the case with interior control.

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