相关论文: Discrete energy estimates for the abcd-systems

This paper develops high-order well-balanced (WB) energy stable (ES) finite difference schemes for multi-layer (the number of layers $M\geqslant 2$) shallow water equations (SWEs) on both fixed and adaptive moving meshes, extending our…

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…

A second-order backward differentiation formula (BDF2) finite-volume discretization for a nonlinear cross-diffusion system arising in population dynamics is studied. The numerical scheme preserves the Rao entropy structure and conserves the…

Maintaining conservation laws in the fully discrete setting is critical for accurate long-time behavior of numerical simulations and requires accounting for discrete conservation properties in both space and time. This paper derives…

This article emphasizes on inconsistencies in the dynamical estimates obtained by first-order transverse discontinuity mapping (TDM) and direct numerical observations for hybrid dynamical systems. Pitfalls of locally linearizing hybrid…

This paper develops and analyzes an optimal-order semi-discrete scheme and its fully discrete finite element approximation for nonlinear stochastic elastic wave equations with multiplicative noise. A non-standard time-stepping scheme is…

We study an implicit finite-volume scheme for non-linear, non-local aggregation-diffusion equations which exhibit a gradient-flow structure, recently introduced by Bailo, Carrillo, and Hu (2020). Crucially, this scheme keeps the dissipation…

We analyze a semi-implicit finite volume scheme for the Gray--Scott system, a model for pattern formation in chemical and biological media. We prove unconditional well-posedness of the fully discrete problem and establish qualitative…

In this paper, we propose a finite-volume scheme for aggregation-diffusion equations based on a Scharfetter--Gummel approximation of the quadratic, nonlocal flux term. This scheme is analyzed concerning well-posedness and convergence…

In this paper, we study the problem of computing the effective diffusivity for particles moving in chaotic flows. Instead of solving a convection-diffusion type cell problem in the Eulerian formulation (arising from homogenization theory…

A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the…

We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial…

Methods of the explicitly correlated F12 approach are applied to the problem of calculating the uncoupled second-order dispersion energy in symmetry-adapted perturbation theory. The accuracy of the new method is tested for noncovalently…

In this paper, we will provide the the finite element method for the electro-osmotic flow in micro-channels, in which a convection-diffusion type equation is given for the charge density $\rho^e$. A time-discrete method based on the…

In this work we present the convergence of a positivity preserving semi-discrete finite volume scheme for a coupled system of two non-local partial differential equations with cross-diffusion. The key to proving the convergence result is to…

In this paper, by introducing two temporal-derivative-dependent auxiliary variables, a linearized and decoupled fourth-order compact finite difference method is developed and analyzed for the nonlinear coupled bacterial systems. The…

This paper is concerned with the construction of high order schemes on irregular grids for balance laws, including a discussion of an a-posteriori error indicator based on the numerical entropy production. We also impose well-balancing on…

The aim of this work is to propose a provably convergent finite volume scheme for the so-called Stefan-Maxwell model, which describes the evolution of the composition of a multi-component mixture and reads as a cross-diffusion system. The…

In this paper we propose an explicit two-level conservative scheme based on a TE/TM like splitting of the field components in time. Its dispersion properties are adjusted to accelerator problems. It is simpler and faster than the implicit…

We introduce a robust optimization method for flip-free distortion energies used, for example, in parametrization, deformation, and volume correspondence. This method can minimize a variety of distortion energies, such as the symmetric…