
Implicitexplicit BDF k SAV schemes for general dissipative systems and their error analysis
We construct efficient implicitexplicit BDFk scalar auxiliary variable ...
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Error Inhibiting Schemes for Initial Boundary Value Heat Equation
In this paper, we elaborate the analysis of some of the schemes which we...
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High order numerical schemes for transport equations on bounded domains
This article is an account of the NABUCO project achieved during the sum...
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A high order fully discrete scheme for the Kortewegde vries equation with a timestepping procedure of RungeKuttacomposition type
We consider the periodic initialvalue problem for the Kortewegde Vries...
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Error analysis for 2D stochastic Navier–Stokes equations in bounded domains
We study a finiteelement based spacetime discretisation for the 2D sto...
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Convergence of the implicit MACdiscretized Navier–Stokes equations with variable density and viscosity on nonuniform grids
The present paper is focused on the proof of the convergence of the disc...
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Numerical approximation of statistical solutions of the incompressible NavierStokes Equations
Statistical solutions, which are timeparameterized probability measures...
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Stability and error analysis of a class of highorder IMEX schemes for Navierstokes equations with periodic boundary conditions
We construct highorder semidiscreteintime and fully discrete (with FourierGalerkin in space) schemes for the incompressible NavierStokes equations with periodic boundary conditions, and carry out corresponding error analysis. The schemes are of implicitexplicit type based on a scalar auxiliary variable (SAV) approach. It is shown that numerical solutions of these schemes are uniformly bounded without any restriction on time step size. These uniform bounds enable us to carry out a rigorous error analysis for the schemes up to fifthorder in a unified form, and derive global error estimates in l^∞(0,T;H^1)∩ l^2(0,T;H^2) in the two dimensional case as well as local error estimates in l^∞(0,T;H^1)∩ l^2(0,T;H^2) in the three dimensional case. We also present numerical results confirming our theoretical convergence rates and demonstrating advantages of higherorder schemes for flows with complex structures in the double shear layer problem.
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