Related papers: Functional a posteriori error estimate for a nonsy…
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…
A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems of Dirichlet and mixed boundary conditions are proposed. Stability and efficiency of the estimators are proved. Finally, we provide…
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…
A posteriori estimates give bounds on the error between the unknown solution of a partial differential equation and its numerical approximation. We present here the methodology based on H1-conforming potential and H(div)-conforming…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…
Based on the auxiliary subspace techniques, a hierarchical basis a posteriori error estimator is proposed for the Stokes problem in two and three dimensions. For the error estimator, we need to solve only two global diagonal linear systems…
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…
This work is focused on the application of functional-type a posteriori error estimates and corresponding indicators to a class of time-dependent problems. We consider the algorithmic part of their derivation and implementation and also…
This paper presents a numerical method to implement the parameter estimation method using response statistics that was recently formulated by the authors. The proposed approach formulates the parameter estimation problem of It\^o drift…
We combine a systematic approach for deriving general a posteriori error estimates for convex minimization problems based on convex duality relations with a recently derived generalized Marini formula. The a posteriori error estimates are…
We consider the a posteriori error estimation for convection-diffusion-reaction equations in both diffusion-dominated and convection/reaction-dominated regimes. We present an explicit hybrid estimator, which, in each regime, is proved to be…
The numerical approximation of convection-dominated problems continues to remain subject of strong interest. Families of stabilization techniques for finite element methods were developed in the past. Adaptive techniques based on a…
Functional error estimates are well-established tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary…
An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing…
This work proposes a new procedure for estimating the non-stationary spatial covariance function for Spatial-Temporal Deformation. The proposed procedure is based on a monotonic function approach. The deformation functions are expanded as a…
This work deals with the a posteriori error estimates for the Darcy-Forchheimer problem. We introduce the corresponding variational formulation and discretize it by using the finite-element method. A posteriori error estimate with two types…
A non-parametric diffusion model with an additive fractional Brownian motion noise is considered in this work. The drift is a non-parametric function that will be estimated by two methods. On one hand, we propose a locally linear estimator…
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…
This work provides reliable a posteriori error estimates for Runge-Kutta discontinuous Galerkin approximations of nonlinear convection-diffusion systems. The classes of systems we study are quite general with a focus on convection-dominated…
In this work we study a residual based a posteriori error estimation for the CutFEM method applied to an elliptic model problem. We consider the problem with non-polygonal boundary and the analysis takes into account the geometry and data…