Optimal Error Estimates of Linearized Crank-Nicolson Galerkin FEMs for the Time-Dependent Ginzburg--Landau Equations in Superconductivity

2014 ◽  
Vol 52 (3) ◽  
pp. 1183-1202 ◽  
Author(s):  
Huadong Gao ◽  
Buyang Li ◽  
Weiwei Sun
Keyword(s):  
Error Estimates ◽  
Time Dependent ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations ◽  
Crank Nicolson

scholarly journals Decoupled Scheme for Time-Dependent Natural Convection Problem II: Time Semidiscreteness

2014 ◽  
Vol 2014 ◽  
pp. 1-23 ◽  
Author(s):  
Tong Zhang ◽  
ZhenZhen Tao
Keyword(s):  
Natural Convection ◽  
Error Estimates ◽  
Numerical Scheme ◽  
Computational Cost ◽  
Time Dependent ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Backward Euler ◽  
Convection Problem ◽  
Natural Convection Problem

We study the numerical methods for time-dependent natural convection problem that models coupled fluid flow and temperature field. A coupled numerical scheme is analyzed for the considered problem based on the backward Euler scheme; stability and the corresponding optimal error estimates are presented. Furthermore, a decoupled numerical scheme is proposed by decoupling the nonlinear terms via temporal extrapolation; optimal error estimates are established. Finally, some numerical results are provided to verify the performances of the developed algorithms. Compared with the coupled numerical scheme, the decoupled algorithm not only keeps good accuracy but also saves a lot of computational cost. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the decoupled method for time-dependent natural convection problem.

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