Related papers: Strictly equivalent a~posteriori error estimators …
In this paper, we present a study of an a posteriori estimator for the discretization error of a non-standard finite difference scheme applied to boundary value problems defined on an infinite interval. In particular, we show how…
We propose an a posteriori error estimator for high-order $p$- or $hp$-finite element discretizations of selfadjoint linear elliptic eigenvalue problems that is appropriate for estimating the error in the approximation of an eigenvalue…
This paper focuses on the analysis of conforming virtual element methods for general second-order linear elliptic problems with rough source terms and applies it to a Poisson inverse source problem with rough measurements. For the forward…
We propose and analyze a reliable and efficient a posteriori error estimator for a constrained linear-quadratic optimal control problem involving Dirac measures; the control variable corresponds to the amplitude of forces modeled as point…
This paper introduces a new computational methodology for determining a-posteriori multi-objective error estimates for finite-element approximations, and for constructing corresponding (quasi-)optimal adaptive refinements of finite-element…
In this paper, we study a modified residual-based a posteriori error estimator for the nonconforming linear finite element approximation to the interface problem. The reliability of the estimator is analyzed by a new and direct approach…
This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…
In a posteriori error analysis, the relationship between error and estimator is usually spoiled by so-called oscillation terms, which cannot be bounded by the error. In order to remedy, we devise a new approach where the oscillation has the…
In this paper we analyze a posteriori error estimates for a mixed formulation of the linear elasticity eigenvalue problem. A posteriori estimators for the nearly and perfectly compressible elasticity spectral problems are proposed. With a…
We propose a cheaper version of \textit{a posteriori} error estimator from arXiv:1707.00057 for the linear second-order wave equation discretized by the Newmark scheme in time and by the finite element method in space. The new estimator…
We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…
Within this article, we develop a residual type a posteriori error estimator for a time discrete quasi-static phase-field fracture model. Particular emphasize is given to the robustness of the error estimator for the variational inequality…
We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…
In this paper, we propose a novel adaptive finite element method for an elliptic equation with line Dirac delta functions as a source term. We first study the well-posedness and global regularity of the solution in the whole domain. Instead…
We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…
We develop a novel a posteriori error estimator for the $L^2$ error committed by the finite element discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi-discretization…
This paper is concerned with the derivation of conforming and non-conforming functional a posteriori error estimates for elliptic boundary value problems in exterior domains. These estimates provide computable and guaranteed upper and lower…
For elliptic interface problems, this paper studies residual-based a posteriori error estimations for various finite element approximations. For the conforming and the Raviart-Thomas mixed elements in two-dimension and for the…
In two dimensions, we propose and analyze an a posteriori error estimator for finite element approximations of the stationary Navier Stokes equations with singular sources on Lipschitz, but not necessarily convex, polygonal domains. Under a…
We consider mixed finite element methods with exact symmetric stress tensors. We derive a new quasi-optimal a priori error estimate uniformly valid with respect to the compressibility. For the a posteriori error analysis we consider the…