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In this paper, we propose and analyze an inexact version of the symmetric proximal alternating direction method of multipliers (ADMM) for solving linearly constrained optimization problems. Basically, the method allows its first subproblem…

This paper derives a posteriori error estimators for the nonlinear first-order optimality conditions associated with the electrically and flexoelectrically coupled Frank-Oseen model of liquid crystals, building on the results of [14] for…

Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…

Abstract. The purpose of this paper is twofold. We introduce the theory of random tensors, which naturally extends the method of random averaging operators in our earlier work arXiv:1910.08492, to study the propagation of randomness under…

This contribution is the numerically oriented companion article of the work [E. Canc\`es, V. Ehrlacher, F. Legoll, B. Stamm and S. Xiang, arxiv preprint 1807.05131]. We focus here on the numerical resolution of the embedded corrector…

This paper addresses the complexity reduction of stochastic homogenisation of a class of random materials for a stationary diffusion equation. A cost-efficient approximation of the correctors is built using a method designed to exploit…

In this paper a technique is given to recover the classical order of the method when explicit exponential Runge-Kutta methods integrate reaction-diffusion problems. Although methods of high stiff order for problems with vanishing boundary…

Nonstationary and nonequilibrium processes are considered on the basis of an Enskog-Landau kinetic equation using a boundary conditions method. A nonstationary solution of this equation is found in the pair collision approximation. This…

We present a method of deriving two boundary conditions at a thin membrane for diffusion from experimental data. This method can be really useful in complex membrane systems in which we do not know mechanisms of processes occurring within…

We consider a nonlinear boundary value problem driven by a nonhomogeneous differential operator. The problem exhibits competing nonlinearities with a superlinear (convex) contribution coming from the reaction term and a sublinear (concave)…

We study the nonlinear Schr\"odinger equation on the half-line with a boundary condition that involves time derivative. This boundary condition was presented by Zambon [J. High Energ. Phys. 2014 (2014) 36]. We establish the integrability of…

We investigate, both analytically and numerically, dispersive fractalization and quantization of solutions to periodic linear and nonlinear Fermi-Pasta-Ulam-Tsingou systems. When subject to periodic boundary conditions and discontinuous…

The finite difference scheme with the shifted Gr\"{u}nwarld formula is employed to semi-discrete the fractional diffusion equations. This spatial discretization can reduce to the large system of ordinary differential equations (ODEs) with…

This paper considers the numerical analysis of a semilinear fractional diffusion equation with nonsmooth initial data. A new Gr\"onwall's inequality and its discrete version are proposed. By the two inequalities, error estimates in three…

We study the interior and exterior contact problems for hemitropic elastic solids. We treat the cases when the friction effects, described by Tresca friction (given friction model), are taken into consideration either on some part of the…

We study the symmetry reduction of nonlinear partial differential equations which are used for describing diffusion processes in nonhomogeneous medium. We find ansatzes reducing partial differential equations to systems of ordinary…

This paper is about how we study statistical methods. As an example, it uses the random regressions model, in which the intercept and slope of cluster-specific regression lines are modeled as a bivariate random effect. Maximizing this…

Extrapolation methods use the last few iterates of an optimization algorithm to produce a better estimate of the optimum. They were shown to achieve optimal convergence rates in a deterministic setting using simple gradient iterates. Here,…

The aim of this paper is to construct and analyze explicit exponential Runge-Kutta methods for the temporal discretization of linear and semilinear integro-differential equations. By expanding the errors of the numerical method in terms of…

A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…