相关论文: An entropy admissible time splitting scheme for a …
In this paper, we are concerned with a operator splitting scheme for linear fractional and fractional degenerate stochastic conservation laws driven by multiplicative Levy noise. More specifically, using a variant of classical Kruzkov's…
We consider the numerical integration of conservation laws endowed with an entropy inequality and we study the residual of the scheme on this inequality, which represents the numerical entropy production. This idea has been introduced and…
We analyze a semi-discrete splitting method for conservation laws driven by a semilinear noise term. Making use of fractional $BV$ estimates, we show that the splitting method produces a compact sequence of approximate solutions converging…
Entropy solutions have been widely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in \cite{CDL1,CDL2} have demonstrated that entropy solutions may not be…
We consider well-balanced schemes for the following 1D scalar conservation law with source term: d_t u + d_x f(u) + z'(x) b(u) = 0. More precisely, we are interested in the numerical approximation of the initial boundary value problem for…
We consider a semi-discrete finite volume scheme for a degenerate fractional conservation laws driven by a cylindrical Wiener process. Making use of the bounded variation (BV) estimates, Young measure theory, and a clever adaptation of…
Stable numerical simulations for a hyperbolic system of conservation laws of relaxation type but not in divergence form are obtained by incorporating the physical entropy into the simulations. The entropy balance is utilized as an…
In this paper, we analyze a semi-discrete finite difference scheme for a conservation laws driven by a homogeneous multiplicative Levy noise. Thanks to BV estimates, we show a compact sequence of approximate solutions, generated by the…
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which detailed balance and time-reversal symmetry are broken. Despite…
We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our…
We propose a fully discretised numerical scheme for the hyperelastic rod wave equation on the line. The convergence of the method is established. Moreover, the scheme can handle the blow-up of the derivative which naturally occurs for this…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
A semi-implicit in time, entropy stable finite volume scheme for the compressible barotropic Euler system is designed and analyzed and its weak convergence to a dissipative measure-valued (DMV) solution [E. Feireisl et al., Dissipative…
We consider entropy conservative and dissipative discretizations of nonlinear conservation laws with implicit time discretizations and investigate the influence of iterative methods used to solve the arising nonlinear equations. We show…
The moment of entropy equation for vector-BGK model results in the entropy equation for macroscopic model. However, this is usually not the case in numerical methods because the current literature consists only of entropy conserving/stable…
This article deals with the error estimates for numerical approximations of the entropy solutions of coupled systems of nonlocal hyperbolic conservation laws. The systems can be strongly coupled through the nonlocal coefficient present in…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
We are interested in the approximation of a steady hyperbolic problem. In some cases, the solution can satisfy an additional conservation relation, at least when it is smooth. This is the case of an entropy. In this paper, we show, starting…
In this paper, we study the large--time behavior of a numerical scheme discretizing drift-- diffusion systems for semiconductors. The numerical method is finite volume in space, implicit in time, and the numerical fluxes are a…
A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial…