Optimal Error Estimates of Semi-implicit Galerkin Method for Time-Dependent Nematic Liquid Crystal Flows

2017 ◽  
Vol 74 (2) ◽  
pp. 979-1008 ◽  
Author(s):  
Rong An ◽  
Jian Su
Keyword(s):  
Liquid Crystal ◽  
Galerkin Method ◽  
Error Estimates ◽  
Nematic Liquid Crystal ◽  
Time Dependent ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Nematic Liquid Crystal Flows

scholarly journals AnH1-Galerkin method for a Stefan problem with a quasilinear parabolic equation in non-divergence form

1987 ◽  
Vol 10 (2) ◽  
pp. 345-360 ◽  
Author(s):  
A. K. Pani ◽  
P. C. Das
Keyword(s):  
Parabolic Equation ◽  
Galerkin Method ◽  
Error Estimates ◽  
Stefan Problem ◽  
Single Phase ◽  
Quasilinear Parabolic Equation ◽  
Divergence Form ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Quasilinear Parabolic

Optimal error estimates inL2,H1andH2-norm are established for a single phase Stefan problem with quasilinear parabolic equation in non-divergence form by anH1-Galerkin procedure.

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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