相关论文: An asymptotically stable scheme for diffusive coag…
We address an original approach for the convergence analysis of a finite-volume scheme for the approximation of a stochastic diffusion-convection equation with multiplicative noise in a bounded domain of $\mathbb{R}^d$ (with $d=2$ or $3$)…
In this work, we consider the numerical recovery of a spatially dependent diffusion coefficient in a subdiffusion model from distributed observations. The subdiffusion model involves a Caputo fractional derivative of order $\alpha\in(0,1)$…
A discretization scheme is introduced for a set of convection-diffusion equations with a non-linear reaction term, where the convection velocity is constant for each reactant. This constancy allows a transformation to new spatial variables,…
In this work we propose a nonlinear stabilization technique for convection-diffusion-reaction and pure transport problems discretized with space-time isogeometric analysis. The stabilization is based on a graph-theoretic artificial…
Various classes of stable finite difference schemes can be constructed to obtain a numerical solution. It is important to select among all stable schemes such a scheme that is optimal in terms of certain additional criteria. In this study,…
This paper detailedly discusses the locally one-dimensional numerical methods for efficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional…
We study necessary conditions for stability of a Numerov-type compact higher-order finite-difference scheme for the 1D homogeneous wave equation in the case of non-uniform spatial meshes. We first show that the uniform in time stability…
We study a two-point flux approximation finite volume scheme for a cross-diffusion system. The scheme is shown to preserve the key properties of the continuous systems, among which the decay of the entropy. The convergence of the scheme is…
Stable distributions are an important class of infinitely-divisible probability distributions, of which two special cases are the Cauchy distribution and the normal distribution. Aside from a few special cases, the density function for…
We consider an advection-diffusion equation that is both non-coercive and advection-dominated. We present a possible numerical approach, to our best knowledge new, and based on the invariant measure associated to the original equation. The…
We introduce a finite volume scheme to solve a special case of isotropic 3-wave kinetic equations. We test our numerical solution against theoretical results concerning the long time behavior of the energy and observe that our solutions…
Mathematical modeling of fluid dynamics for computer graphics requires high levels of theoretical rigor to ensure visually plausible and computationally efficient simulations. This paper presents an in-depth theoretical framework analyzing…
This paper introduces improved numerical techniques for addressing numerical boundary and interface coupling conditions in the context of diffusion equations in cellular biophysics or heat conduction problems in fluid-structure…
This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability…
Convection-diffusion problem are the base for continuum mechanics. The main features of these problems are associated with an indefinite operator the problem. In this work we construct unconditionally stable scheme for non-stationary…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
In this work we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists on two fully coupled, non-linear equations: a degenerate parabolic equation and an elliptic equation. The proposed…
We present a Finite Volume formulation for determining discontinuous distributions of magnetic fields within non-orthogonal and non-uniform meshes. The numerical approach is based on the discretization of the vector potential variant of the…
This article deals with the convergence of finite volume scheme (FVS) for solving coagulation and multiple fragmentation equations having locally bounded coagulation kernel but singularity near the origin due to fragmentation rates. Thanks…
We consider a general family of nonlocal in space and time diffusion equations with space-time dependent diffusivity and prove convergence of finite difference schemes in the context of viscosity solutions under very mild conditions. The…