24 research outputs found
Convergence of fully discrete schemes for diffusive dispersive conservation laws with discontinuous coefficient
We are concerned with fully-discrete schemes for the numerical approximation
of diffusive-dispersive hyperbolic conservation laws with a discontinuous flux
function in one-space dimension. More precisely, we show the convergence of
approximate solutions, generated by the scheme corresponding to vanishing
diffusive-dispersive scalar conservation laws with a discontinuous coefficient,
to the corresponding scalar conservation law with discontinuous coefficient.
Finally, the convergence is illustrated by several examples. In particular, it
is delineated that the limiting solutions generated by the scheme need not
coincide, depending on the relation between diffusion and the dispersion
coefficients, with the classical Kruzkov-Oleinik entropy solutions, but contain
nonclassical undercompressive shock waves.Comment: 38 Pages, 6 figure
Continuous dependence estimate for a degenerate parabolic-hyperbolic equation with Levy noise
In this article, we are concerned with a multidimensional degenerate
parabolic-hyperbolic equation driven by Levy processes. Using bounded variation
(BV) estimates for vanishing viscosity approximations, we derive an explicit
continuous dependence estimate on the nonlinearities of the entropy solutions
under the assumption that Levy noise depends only on the solution. This result
is used to show the error estimate for the stochastic vanishing viscosity
method. In addition, we establish fractional BV estimate for vanishing
viscosity approximations in case the noise coefficients depend on both the
solution and spatial variable.Comment: 31 Pages. arXiv admin note: text overlap with arXiv:1502.0249
Finite difference schemes for the symmetric Keyfitz-Kranzer system
We are concerned with the convergence of numerical schemes for the initial
value problem associated to the Keyfitz-Kranzer system of equations. This
system is a toy model for several important models such as in elasticity
theory, magnetohydrodynamics, and enhanced oil recovery. In this paper we prove
the convergence of three difference schemes. Two of these schemes is shown to
converge to the unique entropy solution. Finally, the convergence is
illustrated by several examples.Comment: 31 page