相关论文: Discrete energy estimates for the abcd-systems
This paper proposes a new class of mass or energy conservative numerical schemes for the generalized Benjamin-Ono (BO) equation on the whole real line with arbitrarily high-order accuracy in time. The spatial discretization is achieved by…
This article introduces a novel numerical approach, based on Finite Volume Techniques, for studying fully nonlinear coagulation-fragmentation models, where both the coagulation and fragmentation components of the collision operator are…
High-order accurate summation-by-parts (SBP) finite difference (FD) methods constitute efficient numerical methods for simulating large-scale hyperbolic wave propagation problems. Traditional SBP FD operators that approximate first-order…
This paper is concerned with the numerical analysis of the explicit upwind finite volume scheme for numerically solving continuity equations. We are interested in the case where the advecting velocity field has spatial Sobolev regularity…
We study the convergence rate of a class of linear multi-step methods for BSDEs. We show that, under a sufficient condition on the coefficients, the schemes enjoy a fundamental stability property. Coupling this result to an analysis of the…
We introduce a new class of finite differences schemes to approximate one dimensional dissipative semilinear hyperbolic systems with a BGK structure. Using precise analytical time-decay estimates of the local truncation error, it is…
An initial-boundary value problem for the $n$-dimensional wave equation is considered. A three-level explicit in time and conditionally stable 4th-order compact scheme constructed recently for $n=2$ and the square mesh is generalized to the…
An explicit numerical scheme is proposed for solving the initial-boundary value problem for the radiative transport equation in a rectangular domain with completely absorbing boundary condition. An upwind finite difference approximation is…
We present rigorous error estimates towards a first-order unconditionally energy stable scheme designed for 3D hydrodynamic Q-tensor model of nematic liquid crystals. This scheme combines the scalar auxiliary variable (SAV), stabilization…
In this article, a numerical scheme is introduced for solving the fractional partial differential equation (FPDE) arising from electromagnetic waves in dielectric media (EMWDM) by using an efficient class of finite difference methods. The…
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…
In this study, we introduce a refined method for ascertaining error estimations in numerical simulations of dynamical systems via an innovative application of composition techniques. Our approach involves a dual application of a basic…
A new second-order numerical scheme based on an operator splitting is proposed for the Godunov-Peshkov-Romenski model of continuum mechanics. The homogeneous part of the system is solved with a finite volume method based on a WENO…
We analyze the wave equation in mixed form, with periodic and/or Dirichlet homogeneous boundary conditions, and nonconstant coefficients that depend on the spatial variable. For the discretization, the weak form of the second equation is…
In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation…
We present a new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which simultaneously gives an approximation of the solution and of its gradient. In the case of simplicial meshes, the…
We consider a problem of nuclear waste contamination. It takes into account the thermal effects. The temperature and the contaminant's concentration fulfill convection-diffusion-reaction equations. The velocity and the pressure in the flow…
In this paper, we present an error estimate of a second-order linearized finite element (FE) method for the 2D Navier-Stokes equations with variable density. In order to get error estimates, we first introduce an equivalent form of the…
We consider the numerical solution of coupled volume-surface reaction-diffusion systems having a detailed balance equilibrium. Based on the conservation of mass, an appropriate quadratic entropy functional is identified and an…
Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…