Numerical analysis of the Crank-Nicolson extrapolation time discrete scheme for magnetohydrodynamics flows

2015 ◽  
Vol 31 (6) ◽  
pp. 2169-2208 ◽  
Author(s):  
Yuhong Zhang ◽  
Yanren Hou ◽  
Li Shan
Keyword(s):  
Numerical Analysis ◽  
Discrete Scheme ◽  
Crank Nicolson

NUMERICAL ANALYSIS OF A MINIMAX OPTIMAL CONTROL PROBLEM WITH AN ADDITIVE FINAL COST

2002 ◽  
Vol 12 (02) ◽  
pp. 183-203 ◽  
Author(s):  
LAURA S. ARAGONE ◽  
SILVIA C. DI MARCO ◽  
ROBERTO L. V. GONZÁLEZ
Keyword(s):  
Optimal Control ◽  
Numerical Analysis ◽  
Optimal Control Problem ◽  
Convergence Rate ◽  
Control Problem ◽  
Discrete Solution ◽  
Discrete Scheme ◽  
Fully Discrete ◽  
Minimax Optimal Control ◽  
Continuous Problem

In this paper we deal with the numerical analysis of an optimal control problem of minimax type with finite horizon and final cost. To get numerical approximations we devise here a fully discrete scheme which enables us to compute an approximated solution. We prove that the fully discrete solution converges to the solution of the continuous problem and we also give the order of the convergence rate. Finally we present some numerical results.

ON FULLY DISCRETE GALERKIN APPROXIMATIONS FOR THE CAHN‐HILLIARD EQUATION

2004 ◽  
Vol 9 (4) ◽  
pp. 313-326 ◽  
Author(s):  
K. Omrani
Keyword(s):  
Galerkin Approximation ◽  
Second Order ◽  
Discrete Scheme ◽  
Fully Discrete ◽  
Hilliard Equation ◽  
Galerkin Approximations ◽  
Cahn Hilliard Equation ◽  
Nicolson Scheme ◽  
Crank Nicolson

Standard Galerkin approximations, using smooth splines to solutions of the nonlinear evolutionary Cahn‐Hilliard equation are analysed. The existence, uniqueness and convergence of the fully discrete Crank‐Nicolson scheme are discussed. At last a linearized Galerkin approximation is presented, which is also second order accurate in time fully discrete scheme.

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