scholarly journals Optimal Error Estimates of Galerkin Finite Element Methods for Stochastic Allen–Cahn Equation with Additive Noise

2019 ◽  
Vol 80 (2) ◽  
pp. 1171-1194 ◽  
Author(s):  
Ruisheng Qi ◽  
Xiaojie Wang
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Finite Element Methods ◽  
Additive Noise ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Galerkin Finite Element ◽  
Cahn Equation ◽  
Galerkin Finite Element Methods

Two-Grid Finite Element Methods for the Steady Navier-Stokes/Darcy Model

2016 ◽  
Vol 6 (1) ◽  
pp. 60-79 ◽  
Author(s):  
Jing Zhao ◽  
Tong Zhang
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Finite Element Methods ◽  
Navier Stokes ◽  
Optimal Error Estimates ◽  
Numerical Computations ◽  
Optimal Error ◽  
Darcy Model ◽  
Efficiency And Effectiveness ◽  
Grid Algorithm

AbstractTwo-grid finite element methods for the steady Navier-Stokes/Darcy model are considered. Stability and optimal error estimates in the H1-norm for velocity and piezometric approximations and the L2-norm for pressure are established under mesh sizes satisfying h = H2. A modified decoupled and linearised two-grid algorithm is developed, together with some associated optimal error estimates. Our method and results extend and improve an earlier investigation, and some numerical computations illustrate the efficiency and effectiveness of the new algorithm.

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