Related papers: Robust error estimates in weak norms for advection…
A posteriori estimates for mixed finite element discretizations of the Navier-Stokes equations are derived. We show that the task of estimating the error in the evolutionary Navier-Stokes equations can be reduced to the estimation of the…
This paper is concerned with the optimized Schwarz waveform relaxation method and Ventcel transmission conditions for the linear advection-diffusion equation. A mixed formulation is considered in which the flux variable represents both…
We present and analyze an a posteriori error estimator for a space-time hybridizable discontinuous Galerkin discretization of the time-dependent advection-diffusion problem. The residual-based error estimator is proven to be reliable and…
The convection-diffusion eigenvalue problems are hot topics, and computational mathematics community and physics community are concerned about them in recent years. In this paper, we consider the a posteriori error analysis and the adaptive…
The effect of advection on the critical minimal speed of traveling waves is studied. Previous theoretical studies estimated the effect on the velocity of stable fast waves and predicted the existence of a critical advection strength below…
Disruption-generated runaway electrons (RE) present an outstanding issue for ITER. The predictive computational studies of RE generation rely on orbit-averaged computations and, as such, they lack the effects from the magnetic field…
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…
The calculation of transport profiles from experimental measurements belongs in the category of inverse problems which are known to come with issues of ill-conditioning or singularity. A reformulation of the calculation, the matricial…
Recent works showed that pressure-robust modifications of mixed finite element methods for the Stokes equations outperform their standard versions in many cases. This is achieved by divergence-free reconstruction operators and results in…
We present a machine learning framework that blends image super-resolution technologies with passive, scalar transport in the level-set method. Here, we investigate whether we can compute on-the-fly, data-driven corrections to minimize…
We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. The steady-state diffusive flux in a finite system subject to a concentration gradient is…
In this work we derive a posteriori error estimates for the convection-diffusion-reaction equation coupled with the Darcy-Forchheimer problem by a nonlinear external source depending on the concentration of the fluid. We introduce the…
We consider a moving boundary problem with kinetic condition that describes the diffusion of solvent into rubber and study semi-discrete finite element approximations of the corresponding weak solutions. We report on both a priori and a…
We consider systems of ordinary differential equations with multiple scales in time. In general, we are interested in the long time horizon of a slow variable that is coupled to solution components that act on a fast scale. Although the…
We consider a singularly perturbed convection-diffusion problem that has in addition a shift term. We show a solution decomposition using asymptotic expansions and a stability result. Based upon this we provide a numerical analysis of high…
In the flow and transport numerical simulation, mesh adaptivity strategy is important in reducing the usage of CPU time and memory. The refinement based on the pressure error estimator is commonly-used approach without considering the flux…
Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in…
We study the a priori error analysis of finite element methods for Biot's consolidation model. We consider a formulation which has the stress tensor, the fluid flux, the solid displacement, and the pore pressure as unknowns. Two mixed…
A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector…
Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit…