相关论文: A MUSCL-Hancock scheme for non-local conservation …
This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted…
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…
Conservation and consistency are fundamental properties of discretizations of systems of hyperbolic conservation laws. Here, these concepts are extended to the realm of iterative methods by formally defining locally conservative and flux…
We establish a well-posedness and error-estimation framework that solves Hamilton-Jacobi equations by minimizing the least-squares residual of monotone finite-difference discretizations. This approach also applies naturally to second-order…
We are interested in the numerical approximation of discontinuous solutions in non conservative hyperbolic systems. An extension to second-order of a new strategy based on in-cell discontinuous reconstructions to deal with this challenging…
We present a novel positive kinetic scheme built on the efficient collide-and-stream algorithm of the lattice Boltzmann method (LBM) to address hyperbolic conservation laws. We focus on the compressible Euler equations with strong…
We establish local-in-time existence and uniqueness results for nonlocal conservation laws with a nonlinear mobility, in several space dimensions, under weak assumptions on the kernel, which is assumed to be bounded and of finite total…
We propose efficient numerical algorithms for approximating statistical solutions of scalar conservation laws. The proposed algorithms combine finite volume spatio-temporal approximations with Monte Carlo and multi-level Monte Carlo…
This paper provides a convergence analysis for generalized Hamiltonian Monte Carlo samplers, a family of Markov Chain Monte Carlo methods based on leapfrog integration of Hamiltonian dynamics and kinetic Langevin diffusion, that encompasses…
We prove the well-posedness of entropy weak solutions for a class of space-discontinuous scalar conservation laws with non-local flux arising in traffic modeling. We approximate the problem adding a viscosity term and we provide $L^\infty$…
Accurate characterization of entropy plays a pivotal role in capturing reversible and irreversible heating in supercapacitors during charging/discharging cycles. However, numerical methods that can faithfully capture entropy variation in…
The solution of time-dependent hyperbolic conservation laws on cut cell meshes causes the small cell problem: standard schemes are not stable on the arbitrarily small cut cells if an explicit time stepping scheme is used and the time step…
In this paper we study the convergence of a second order finite volume approximation of the scalar conservation law. This scheme is based on the generalized Riemann problem (GRP) solver. We firstly investigate the stability of the GRP…
In this article we study the numerical approximation of incompressible miscible displacement problems with a linearised Crank-Nicolson time discretisation, combined with a mixed finite element and discontinuous Galerkin method. At the heart…
We present a novel implicit scheme for the numerical solution of time-dependent conservation laws. The core idea of the presented method is to exploit and approximate the mixed spatial-temporal derivative of the solution that occurs…
Underdamped Langevin Monte Carlo (ULMC) is an algorithm used to sample from unnormalized densities by leveraging the momentum of a particle moving in a potential well. We provide a novel analysis of ULMC, motivated by two central questions:…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
In this paper, we discretize the Caputo time derivative of order \alpha \in (0,1) using the Alikhanov scheme on a quasi-graded temporal mesh, and employ the Newton linearization method to approximate the nonlinear term. This yields a…
We establish a notion of random entropy solution for degenerate fractional conservation laws incorporating randomness in the initial data, convective flux and diffusive flux. In order to quantify the solution uncertainty, we design a…
Lax-Wendroff Flux Reconstruction (LWFR) is a single-stage, high order, quadrature free method for solving hyperbolic conservation laws. We develop a subcell based limiter by blending LWFR with a lower order scheme, either first order finite…