Related papers: Functional A Posteriori Error Control for Conformi…
In this work, a space-time scheme for goal-oriented a posteriori error estimation is proposed. The error estimator is evaluated using a partition-of-unity dual-weighted residual method. As application, a low mach number combustion equation…
We consider a viscous approximation for a nonlinear degenerate convection-diffusion equations in two space dimensions, and prove an $L^1$ error estimate. Precisely, we show that the $L^1_{\mathrm{loc}}$ difference between the approximate…
We shall establish the convergence of an adaptive conforming finite element method for the reconstruction of the distributed flux in a diffusion system. The adaptive method is based on a posteriori error estimators for the distributed flux,…
This paper presents a goal-oriented a posteriori error estimation framework for linear functionals in the stabilized finite element discretization of the stationary convection-diffusion-reaction (CDR) equation. The theoretical framework for…
In this paper, error estimates are presented for a certain class of optimal control problems with elliptic PDE-constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state…
This work introduces a new approximate proximal sampler that operates solely with zeroth-order information of the potential function. Prior theoretical analyses have revealed that proximal sampling corresponds to alternating forward and…
We consider the optimal control problem governed by diffusion convection reaction equation without control constraints. The proper orthogonal decomposition(POD) method is used to reduce the dimension of the problem. The POD method may be…
We consider similarity solutions of the generalized convection-diffusion-reaction equation with both space- and time-dependent convection, diffusion and reaction terms. By introducing the similarity variable, the reaction-diffusion equation…
This paper focuses on a posteriori error estimates for a pressure-robust finite element method, which incorporates a divergence-free reconstruction operator, within the context of the distributed optimal control problem constrained by the…
In a general setting, we study a posteriori estimates used in finite element analysis to measure the error between a solution and its approximation. The latter is not necessarily generated by a finite element method. We show that the error…
We propose and analyze a goal-oriented a posteriori error estimator for the atomistic-continuum modeling error in the quasicontinuum method. Based on this error estimator, we develop an algorithm which adaptively determines the atomistic…
Accurate error estimation is crucial in model order reduction, both to obtain small reduced-order models and to certify their accuracy when deployed in downstream applications such as digital twins. In existing a posteriori error estimation…
We consider mixed finite element approximation of a singularly perturbed fourth-order elliptic problem with two different boundary conditions, and present a new measure of the error, whose components are balanced with respect to the…
A system of diffusion-reaction equations coupled with a dissolution-precipitation model is discussed. We start by introducing a microscale model together with its homogenized version. In the present paper, we first derive the corrector…
An a posteriori error bound for the pointwise error of the quadratic discontinuous Galerkin method for the unilateral contact problem on polygonal domain is presented. The pointwise a posteriori error analysis is based on the direct use of…
The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent…
We propose and analyze a posteriori error estimators for an optimal control problem that involves an elliptic partial differential equation as state equation and a control variable that enters the state equation as a coefficient; pointwise…
This paper derives an a posteriori error estimator for the nonlinear first-order optimality conditions associated with the electrically and flexoelectrically coupled Frank-Oseen model of liquid crystals, building on previous results for…
We propose a novel a-posteriori error estimation technique where the target quantities of interest are ratios of high-dimensional integrals, as occur e.g. in PDE constrained Bayesian inversion and PDE constrained optimal control subject to…
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…