相关论文: An explicit-implicit Generalized Finite Difference…

Experimental and field investigations for solution mining processes have improved intensely in recent years. Due to today's computing capacities, three-dimensional simulations of potential salt solution caverns can further enhance the…

We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…

We propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages. In the…

We develop a family of stabilized backward differentiation formula (sBDF) schemes of orders one through four for semilinear parabolic equations. The proposed methods are designed to achieve three properties that are rarely available…

Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…

In this paper implicit and explicit exact difference schemes (EDS) for system $\textbf{x}' = A\textbf{x}$ of three linear differential equations with constant coefficients are constructed. Numerical simulations for stiff problem and for…

We present an explicit second order staggered finite difference (FD) discretization scheme for forward simulation of natural gas transport in pipeline networks. By construction, this discretization approach guarantees that the conservation…

In this paper, we consider a nonlinear PDE system governed by a parabolic heat equation coupled in a nonlinear way with a hyperbolic momentum equation describing the behavior of a displacement field coupled with a nonlinear elliptic…

In this paper, we develop sixth-order hybrid finite difference methods (FDMs) for the elliptic interface problem $-\nabla \cdot( a\nabla u)=f$ in $\Omega\backslash \Gamma$, where $\Gamma$ is a smooth interface inside $\Omega$. The variable…

In this study, we propose a new scheme named as complete flux scheme (CFS) based on the finite volume method for solving singularly perturbed differential-difference equations (SPDDEs) of elliptic type. An alternate integral representation…

We propose a multiscale spectral generalized finite element method (MS-GFEM) for discontinuous Galerkin (DG) discretizations. The method builds local approximations on overlapping subdomains as the sum of a local source solution and a…

In this paper, an upwind GFDM is developed for the coupled heat and mass transfer problems in porous media. GFDM is a meshless method that can obtain the difference schemes of spatial derivatives by using Taylor expansion in local node…

We present a multiscale mixed finite element method for solving second order elliptic equations with general $L^{\infty}$-coefficients arising from flow in highly heterogeneous porous media. Our approach is based on a multiscale spectral…

We propose finite difference methods for degenerate fully nonlinear elliptic equations and prove the convergence of the schemes. Our focus is on the pure equation and a related free boundary problem of transmission type. The cornerstone of…

Paraxial diffraction modeling based on the Fourier transform has seen widespread implementation for simulating the response of a diffraction-limited optical system. For systems where the paraxial assumption is not sufficient, a class of…

In this article, we introduce a three-precision formulation of the General Alternating-Direction Implicit method (GADI) designed to accelerate the solution of large-scale sparse linear systems $Ax=b$. GADI is a framework that can represent…

We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does not suffer from small cell stiffness. Our discretization is efficient for the wave, heat…

We study the generalized forward-reflected-backward (GFRB) method, an extension of the forward-reflected-backward (FRB) scheme due to Malitsky and Tam, for solving monotone inclusion problems in real Hilbert spaces. We first analyze GFRB…

For elliptic interface problems with discontinuous coefficients, the maximum accuracy order for compact 9-point finite difference scheme in irregular points is three [7]. The discontinuous coefficients usually have abrupt jumps across the…

This paper applies the gradient discretisation method (GDM) for fourth order elliptic variational inequalities. The GDM provides a new formulation of error estimates and a complete convergence analysis of several numerical methods. We show…