Total variation and error estimates for spectral viscosity approximations

Total Variation and Error Estimates for Spectral Viscosity Approximations

We study the behavior of spectral viscosity approximations to nonlinear scalar conservation laws. We show how the spectral viscosity method compromises between the total-variation bounded viscosity approximations— which are restricted to first-order accuracy—and the spectrally accurate, yet unstable, Fourier method. In particular, we prove that the spectral viscosity method is Ll-stable and hen...

Lp error estimates for projection approximations

We provide an error estimate for the local mean projection approximation in L p([0, τ∗]) for p ∈ [1,+∞[, in terms of the regularity of the underlying grid, and we apply it to the corresponding projection approximation of weakly singular Fredholm integral equations of the second kind. © 2004 Elsevier Ltd. All rights reserved.

Error estimates for approximations from control nets

Spectral Viscosity Approximations to Hamilton-Jacobi Solutions

The spectral viscosity approximate solution of convex Hamilton–Jacobi equations with periodic boundary conditions is studied. It is proved in this paper that the approximation and its gradient remain uniformly bounded, formally spectral accurate, and converge to the unique viscosity solution. The L1-convergence rate of the order 1− ε∀ε > 0 is obtained.

On total variation approximations for random assemblies

The purpose of the present note is to draw reader’s attention to an analytic approach proposed by the author in [8] and refined in [9]. In contrast to the celebrated Flajolet-Odlyzko method (see [4]), it allows to obtain asymptotic formulas for the ratio of coefficients of two power series when separately the coefficients do not have a regular asymptotic behavior as their index increases. Moreo...