Related papers: Robust error estimates in weak norms for advection…
In this work, we propose a residual-based a posteriori error estimator for algebraic flux-corrected (AFC) schemes for stationary convection-diffusion equations. A global upper bound is derived for the error in the energy norm for a general…
We explore why many recently proposed robust estimation problems are efficiently solvable, even though the underlying optimization problems are non-convex. We study the loss landscape of these robust estimation problems, and identify the…
We propose and analyse an augmented mixed finite element method for the Oseen equations written in terms of velocity, vorticity, and pressure with non-constant viscosity and homogeneous Dirichlet boundary condition for the velocity. The…
This paper investigates online algorithms for smooth time-varying optimization problems, focusing first on methods with constant step-size, momentum, and extrapolation-length. Assuming strong convexity, precise results for the tracking…
The aim of this paper is to develop a numerical scheme to approximate evolving interface problems for parabolic equations based on the abstract evolving finite element framework proposed in (C M Elliott, T Ranner, IMA J Num Anal, 41:3,…
Multiscale mixing efficiencies for passive scalar advection are defined in terms of the suppression of variance weighted at various length scales. We consider scalars maintained by temporally steady but spatially inhomogeneous sources,…
We review some recent advances in the field of element-based algebraic stabilization for continuous finite element discretizations of nonlinear hyperbolic problems. The main focus is on multidimensional convex limiting techniques designed…
The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by…
In this paper, we investigate the combination of a linear continuous interior penalty type and a non-linear artificial diffusion stabilisation applied to the transport problem, based on continuous Galerkin finite elements in space. This…
We present goal-oriented a posteriori error estimates for the automatic variationally stable finite element (AVS FE) method for scalar-valued convection-diffusion problems. The AVS-FE method is a Petrov-Galerkin method in which the test…
Transportation occupies one-third of the amount in the logistics costs, and accordingly transportation systems largely influence the performance of the logistics system. This work presents an adaptive data-driven innovative modular approach…
This work assesses both empirically and theoretically, using the performance estimation methodology, how robust different first-order optimization methods are when subject to relative inexactness in their gradient computations. Relative…
We derive computable upper bounds for the difference between an exact solution of the evolutionary convection-diffusion problem and an approximation of this solution. The estimates are obtained by certain transformations of the integral…
We study the linear stability with respect to lateral perturbations of free surface films of polymer mixtures on solid substrates. The study focuses on the stability properties of the stratified and homogeneous steady film states studied in…
Robust estimators and different filtering techniques are proposed and their impact on the determination of a wide range of turbulence quantities is analysed. High-frequency water level measurements in a stepped spillway are used as a case…
In this paper, we introduce and analyse a surface finite element discretization of advection-diffusion equations with uncertain coefficients on evolving hypersurfaces. After stating unique solvability of the resulting semi-discrete problem,…
In this paper, we investigate accelerated first-order methods for smooth convex optimization problems under inexact information on the gradient of the objective. The noise in the gradient is considered to be additive with two possibilities:…
A priori analysis for a generalized local projection stabilized finite element approximations for the solution of an advection-reaction equation is presented in this article. The stability and a priori error estimates are established for…
We perform an exhaustive study of the simplest, nontrivial problem in advection-diffusion -- a finite absorber of arbitrary cross section in a steady two-dimensional potential flow of concentrated fluid. This classical problem has been…
This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational…