相关论文: Convergence of a finite difference scheme for 2X2 …

We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…

There exists a diversity of weak Local Linearization (LL) schemes for the integration of stochastic differential equations with additive noise, which differ with respect to the algorithm that is employed in the numerical implementation of…

The main goal of this paper is twofold. First, we extend some results known in the case of weak greedy algorithms with a scalar parameter to the case of weak greedy algorithms with a weakness sequence. Second, we formulate a new setting of…

In this paper, we revisit the old problem of compact finite difference approximations of the homogeneous Dirichlet problem in dimension 1. We design a large and natural set of schemes of arbitrary high order, and we equip this set with an…

Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially…

We study here the approximation by a finite-volume scheme of a heat equation forced by a Lipschitz continuous multiplicative noise in the sense of It\^o. More precisely, we consider a discretization which is semi-implicit in time and a…

We analyse the asymptotic properties of a continuous-time, two-timescale stochastic approximation algorithm designed for stochastic bilevel optimisation problems in continuous-time models. We obtain the weak convergence rate of this…

In the given paper we consider finite difference approximations to systems of polynomially-nonlinear partial differential equations whose coefficients are rational functions over rationals in the independent variables. The notion of strong…

New variational formulations are devised for the curl--div system, and the corresponding finite element approximations are shown to converge. Curl--free and divergence--free finite elements are employed for discretizing the problem.

We are interested in existence results for second order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal…

In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…

Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…

When using a finite difference method to solve an initial--boundary--value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze…

Difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters $\alpha$ and $\beta$ are considered. By the method of energy inequalities, for the solution…

In this paper we focus on the subdiffusive Black Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model. We derive the governing fractional…

In this paper we prove a rate of convergence for the continuous time filtering solution of a multiple timescale correlated nonlinear system to a lower dimensional filtering equation in the limit of large timescale separation. Correlation is…

This paper is devoted to present an approximation of a Cauchy problem for Friedrichs' systems under convex constraints. It is proved the strong convergence in L^2\_{loc} of a parabolic-relaxed approximation towards the unique constrained…

The aim of this paper is to study the time stepping scheme for approximately solving the subdiffusion equation with a weakly singular source term. In this case, many popular time stepping schemes, including the correction of high-order BDF…

Lattice Boltzmann schemes rely on the enlargement of the size of the target problem in order to solve PDEs in a highly parallelizable and efficient kinetic-like fashion, split into a collision and a stream phase. This structure, despite the…

We propose and analyze a two-level method for mimetic finite difference approximations of second order elliptic boundary value problems. We prove that the two-level algorithm is uniformly convergent, i.e., the number of iterations needed to…