Related papers: A simple predictor-corrector scheme without order …

For linear and fully non-linear diffusion equations of Bellman-Isaacs type, we introduce a class of approximation schemes based on differencing and interpolation. As opposed to classical numerical methods, these schemes work for general…

This work focuses on numerically solving a shape identification problem related to advection-diffusion processes with space-dependent coefficients using shape optimization techniques. Two boundary-type cost functionals are considered, and…

We analyze an advection-diffusion-reaction problem with non-homogeneous boundary conditions that models the chromatography process, a vital stage in bioseparation. We prove stability and error estimates for both constant and affine…

We present a novel approach that redefines the traditional interpretation of explicit and implicit discretization methods for solving a general class of advection-diffusion equations (ADEs) featuring nonlinear advection, diffusion…

In this paper, we suggest a technique to avoid order reduction in time when integrating reaction-diffusion boundary value problems under non-homogeneous boundary conditions with exponential splitting methods. More precisely, we consider…

In this paper, we consider the adaptive Eulerian--Lagrangian method (ELM) for linear convection-diffusion problems. Unlike the classical a posteriori error estimations, we estimate the temporal error along the characteristics and derive a…

We follow-up on our works devoted to homogenization theory for linear second-order elliptic equations with coefficients that are perturbations of periodic coefficients. We have first considered equations in divergence form in [6, 7, 8]. We…

The convergence of Boltzmann Fokker Planck solution can become arbitrarily slow with iterative procedures like source iteration. This paper derives and investigates a nonlinear diffusion acceleration scheme for the solution of the Boltzmann…

Various bias-correction methods such as EXTRA, gradient tracking methods, and exact diffusion have been proposed recently to solve distributed {\em deterministic} optimization problems. These methods employ constant step-sizes and converge…

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…

In this paper, we discuss the 2D convection-diffusion-reaction equation with variable smooth coefficients and the Dirichlet boundary condition on a complicated, thin, and curved domain. We propose the fourth-order compact FDM at every grid…

We present a fast direct solution method for the advection-diffusion equation in one and two dimensions with non-periodic boundaries. Computational cost is reduced to $\mathcal O(N)$ by making a low-rank approximation of the Green's…

This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction--diffusion--advection equation. By using an asymptotic…

We report in this paper the analysis for the linear and nonlinear version of the flux corrected transport (FEM-FCT) scheme in combination with the backward Euler time-stepping scheme applied to time-dependent convection-diffusion-reaction…

We show that the Strang splitting method applied to a diffusion-reaction equation with inhomogeneous general oblique boundary conditions is of order two when the diffusion equation is solved with the Crank-Nicolson method, while order…

Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular,…

Calibrating chemical kinetics in a reaction-diffusion system is challenging because of complex dynamics governed by tightly coupled chemistry and transport, while experimental observations are often sparse and noisy. We propose a physics…

Explicit numerical finite difference schemes for partial differential equations are well known to be easy to implement but they are particularly problematic for solving equations whose solutions admit shocks, blowups and discontinuities.…

Explicit non-oscillatory central difference schemes become excessively diffusive when applied to highly nonlinear advection problems where small time steps are necessary to maintain stability. Here, we present a correction to reduce such…

In this paper, we consider a fast and second-order implicit difference method for approximation of a class of time-space fractional variable coefficients advection-diffusion equation. To begin with, we construct an implicit difference…