Related papers: Guaranteed and computable error bounds for approxi…
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…
The primary objective of this work is to develop coarse-graining schemes for stochastic many-body microscopic models and quantify their effectiveness in terms of a priori and a posteriori error analysis. In this paper we focus on stochastic…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
We present reduced basis approximations and rigorous a posteriori error bounds for the instationary Stokes equations. We shall discuss both a method based on the standard formulation as well as a method based on a penalty approach, which…
This paper develops and discusses a residual-based a posteriori error estimator for parabolic surface partial differential equations on closed stationary surfaces. The full discretization uses the surface finite element method in space and…
We present a detailed study of estimation errors in terms of surrogate loss estimation errors. We refer to such guarantees as $\mathscr{H}$-consistency estimation error bounds, since they account for the hypothesis set $\mathscr{H}$…
Defeaturing, the process of simplifying computational geometries, is a critical step in industrial simulation pipelines for reducing computational cost. Rigorous a posteriori estimators exist for the global energy-norm error introduced by…
The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is…
In this article, we derive \textit{a posteriori} error estimates for the Dirichlet boundary control problem governed by Stokes equation. An energy-based method has been deployed to solve the Dirichlet boundary control problem. We employ an…
Partial differential equations (PDEs) with inputs that depend on infinitely many parameters pose serious theoretical and computational challenges. Sophisticated numerical algorithms that automatically determine which parameters need to be…
We derive optimal order a posteriori error estimates for fully discrete approximations of the initial-boundary value problem for the heat equation. For the discretization in time we apply the fractional-step $\vartheta$-scheme and for the…
We consider the unilateral contact problem between an elastic body and a rigid foundation in a description that includes both Tresca and Coulomb friction conditions. For this problem, we present an a posteriori error analysis based on an…
We perform the a posteriori error analysis of residual type of a transmission problem with sign changing coefficients. According to [6] if the contrast is large enough, the continuous problem can be transformed into a coercive one. We…
We consider systematic numerical approximation of a viscoelastic phase separation model that describes the demixing of a polymer solvent mixture. An unconditionally stable discretisation method is proposed based on a finite element…
This paper is concerned with the recovery of (approximate) solutions to parabolic problems from incomplete and possibly inconsistent observational data, given on a time-space cylinder that is a strict subset of the computational domain…
In this work, we propose an a pointwise a posteriori error estimator for conforming finite element approximations of eigenfunctions corresponding to multiple and clustered eigenvalues of elliptic operators. It is proven that the pointwise a…
We present a computer assisted method for generating existence proofs and a posteriori error bounds for solutions to two point boundary value problems (BVPs). All truncation errors are accounted for and, if combined with interval arithmetic…
This paper presents a strategy for a posteriori error estimation for substructured problems solved by non-overlapping domain decomposition methods. We focus on global estimates of the discretization error obtained through the error in…
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 main goal of this paper is to analyze a family of "simplest possible" initial data for which, as shown by numerical simulations, the incompressible Euler equations have multiple solutions. We take here a first step toward a rigorous…