Related papers: Adapted Lie splitting method for convection-diffus…
In this paper, we present splitting algorithms to solve multicomponent transport models with Maxwell-Stefan-diffusion approaches. The multicomponent models are related to transport problems, while we consider plasma processes, in which the…
We consider the numerical approximation of the ill-posed data assimilation problem for stationary convection-diffusion equations and extend our previous analysis in [Numer. Math. 144, 451--477, 2020] to the convection-dominated regime.…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
In this paper we formulate and analyse adaptive (space-time) least-squares finite element methods for the solution of convection-diffusion equations. The convective derivative $\mathbf{v} \cdot \nabla u$ is considered as part of the total…
We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…
Multilevel Splitting is a Sequential Monte Carlo method to simulate realisations of a rare event as well as to estimate its probability. This article is concerned with the convergence and the fluctuation analysis of Adaptive Multilevel…
We study reinforcement learning for controlled diffusion processes with unbounded continuous state spaces, bounded continuous actions, and polynomially growing rewards: settings that arise naturally in finance, economics, and operations…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
We study time integration schemes for $\dot H^1$-solutions to the energy-(sub)critical semilinear wave equation on $\mathbb{R}^3$. We show first-order convergence in $L^2$ for the Lie splitting and convergence order $3/2$ for a corrected…
A finite difference method is constructed for a singularly perturbed convection diffusion problem posed on an annulus. The method involves combining polar coordinates, an upwind finite difference operator and a piecewise-uniform Shishkin…
Liou-Steffen splitting (AUSM) schemes are popular for low Mach number simulations, however, like many numerical schemes for compressible flow they require careful modification to accurately resolve convective features in this regime.…
The present work proposes a second-order time splitting scheme for a linear dispersive equation with a variable advection coefficient subject to transparent boundary conditions. For its spatial discretization, a dual Petrov--Galerkin method…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
The time-fractional convection-diffusion equation is performed by Lie symmetry analysis method which involves the Riemann-Liouville time-fractional derivative of the order $\alpha\in(0,2)$. In eight cases, the symmetries are obtained and…
We present a new discretization for advection-diffusion problems with Robin boundary conditions on complex time-dependent domains. The method is based on second order cut cell finite volume methods introduced by Bochkov et al. to discretize…
In this paper, a new family of implicit compact finite difference schemes for computation of unsteady convection-diffusion equation with variable convection coefficient is proposed. The schemes are fourth order accurate in space and second…
This paper studies adaptive least-squares finite element methods for convection-dominated diffusion-reaction problems. The least-squares methods are based on the first-order system of the primal and dual variables with various ways of…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance…