
Strong rates of convergence of spacetime discretization schemes for the 2D NavierStokes equations with additive noise
We consider the strong solution of the 2D NavierStokes equations in a t...
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Singular integration towards a spectrally accurate finite difference operator
It is an established fact that a finite difference operator approximates...
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A finite difference method for the variational pLaplacian
We propose a new monotone finite difference discretization for the varia...
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On the convergence rate of the Kačanov scheme for shearthinning fluids
We explore the convergence rate of the Kačanov iteration scheme for diff...
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A convergent FVFEM scheme for the stationary compressible NavierStokes equations
In this paper, we propose a discretization of the multidimensional stat...
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Difference methods for time discretization of stochastic wave equation
The time discretization of stochastic spectral fractional wave equation ...
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A Strongly Consistent Finite Difference Scheme for Steady Stokes Flow and its Modified Equations
We construct and analyze a strongly consistent secondorder finite diffe...
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Convergence and error estimates for a finite difference scheme for the multidimensional compressible NavierStokes system
We prove convergence of a finite difference approximation of the compressible Navier–Stokes system towards the strong solution in R^d,d=2,3, for the adiabatic coefficient γ>1. Employing the relative energy functional, we find a convergence rate which is uniform in terms of the discretization parameters for γ≥ d/2. All results are unconditional in the sense that we have no assumptions on the regularity nor boundedness of the numerical solution. We also provide numerical experiments to validate the theoretical convergence rate. To the best of our knowledge this work contains the first unconditional result on the convergence of a finite difference scheme for the unsteady compressible Navier–Stokes system in multiple dimensions.
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