On optimal convergence rates for higher-order Navier–Stokes approximations. I. Error estimates for the spatial discretization

2005 ◽  
Vol 25 (4) ◽  
pp. 812-841 ◽  
Author(s):  
Markus Bause
Keyword(s):  
Error Estimates ◽  
Convergence Rates ◽  
Higher Order ◽  
Navier Stokes ◽  
Spatial Discretization ◽  
Optimal Convergence ◽  
Optimal Convergence Rates

OPTIMAL CONVERGENCE RATES FOR THE COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH POTENTIAL FORCES

2007 ◽  
Vol 17 (05) ◽  
pp. 737-758 ◽  
Author(s):  
RENJUN DUAN ◽  
SEIJI UKAI ◽  
TONG YANG ◽  
HUIJIANG ZHAO
Keyword(s):  
Convergence Rates ◽  
Stokes Equations ◽  
Initial Perturbation ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Potential Force ◽  
Navier Stokes Equations ◽  
Optimal Convergence ◽  
Whole Space ◽  
Optimal Convergence Rates

For the viscous and heat-conductive fluids governed by the compressible Navier–Stokes equations with an external potential force, there exist non-trivial stationary solutions with zero velocity. By combining the Lp - Lq estimates for the linearized equations and an elaborate energy method, the convergence rates are obtained in various norms for the solution to the stationary profile in the whole space when the initial perturbation of the stationary solution and the potential force are small in some Sobolev norms. More precisely, the optimal convergence rates of the solution and its first order derivatives in L2-norm are obtained when the L1-norm of the perturbation is bounded.

Mixed Schemes for Fourth-Order DIV Equations

2019 ◽  
Vol 19 (2) ◽  
pp. 341-357
Author(s):  
Ronghong Fan ◽  
Yanru Liu ◽  
Shuo Zhang
Keyword(s):  
Theoretical Analysis ◽  
Fourth Order ◽  
Convergence Rates ◽  
Mixed Formulation ◽  
Optimal Convergence ◽  
Mixed Formulations ◽  
Optimal Convergence Rates

AbstractIn this paper, stable mixed formulations are designed and analyzed for the quad div problems under two frameworks presented in [23] and [22], respectively. Analogue discretizations are given with respect to the mixed formulation, and optimal convergence rates are observed, which confirm the theoretical analysis.

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