Related papers: Functional a posteriori error estimate for a nonsy…
We present a fully computable a posteriori error estimator for piecewise linear finite element approximations of reaction-diffusion problems with mixed boundary conditions and piecewise constant reaction coefficient formulated in arbitrary…
In this work, we analyze the residual-based a posteriori error estimation of the multi-scale cancer invasion model, which is a system of three non-stationary reaction-diffusion equations. We present the numerical results of a study on a…
Lower a posteriori error bounds obtained using the standard bubble function approach are reviewed in the context of anisotropic meshes. A numerical example is given that clearly demonstrates that the short-edge jump residual terms in such…
We apply the recent approach of C. Kreuzer and A. Veeser to derive a robust a posteriori error estimator for the reaction-diffusion equation. The estimator together with the corresponding oscillation yields global upper and local lower…
In this study, we employ the variational multiscale (VMS) concept to develop a posteriori error estimates for the stationary convection-diffusion-reaction equation. The variational multiscale method is based on splitting the continuous part…
We propose a new heuristic goal-oriented a posteriori error estimator that connects the dual weighted residual method with equilibrated a posteriori error estimation. Our numerical experiments demonstrate the practical reliability of the…
This paper deals with a copies-based continuously differentiable and strictly decreasing estimator of the drift function for stochastic differential equations defining recurrent diffusion processes. The first part of our paper deals with…
This paper considers the finite element solution of the boundary value problem of Poisson's equation and proposes a guaranteed em a posteriori local error estimation based on the hypercircle method. Compared to the existing literature on…
Consider a Poisson point process with unknown support boundary curve $g$, which forms a prototype of an irregular statistical model. We address the problem of estimating non-linear functionals of the form $\int \Phi(g(x))\,dx$. Following a…
For elliptic interface problems in two- and three-dimensions with a possible very low regularity, this paper establishes a priori error estimates for the Raviart-Thomas and Brezzi-Douglas-Marini mixed finite element approximations. These…
In this paper, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints.…
Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori…
A general a posteriori error analysis applies to five lowest-order finite element methods for two fourth-order semi-linear problems with trilinear non-linearity and a general source. A quasi-optimal smoother extends the source term to the…
This paper is focused on the convergence analysis of an adaptive stochastic collocation algorithm for the stationary diffusion equation with parametric coefficient. The algorithm employs sparse grid collocation in the parameter domain…
We consider energy norm a posteriori error analysis of conforming finite element approximations of singularly perturbed reaction-diffusion problems on simplicial meshes in arbitrary space dimension. Using an equilibrated flux…
The binary Mumford-Shah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision, ranging from basic segmentation and labeling to…
In the recent article [Kopteva, N., Numer. Math., 137, 607--642 (2017)] the author obtained residual-type a posteriori error estimates in the energy norm for singularly perturbed semilinear reaction-diffusion equations on anisotropic…
A posteriori error estimates are constructed for the three-field variational formulation of the Biot problem involving the displacements, the total pressure and the fluid pressure. The discretization under focus is the…
In this article, we present an overview of different a posteriori error analysis and postprocessing methods proposed in the context of nonlinear eigenvalue problems, e.g. arising inelectronic structure calculations for the calculation of…
A residual-based a posteriori error estimator is proposed for the incompressible Oseen problem in the convection-dominated regime. The SUPG/PSPG/grad-div stabilized finite element method is used as discretization. The error estimator…