Related papers: Reduced Basis A Posteriori Error Bounds for Symmet…
In this article, goal-oriented a posteriori error estimation for the biharmonic plate bending problem is considered. The error for approximation of goal functional is represented by an estimator which combines dual-weighted residual method…
A posteriori error estimates in the maximum norm are studied for various time-semidiscretisations applied to a class of linear parabolic equations. We summarise results from the literature and present some new improved error bounds. Crucial…
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…
This article investigates residual a posteriori error estimates and adaptive mesh refinements for time-dependent boundary element methods for the wave equation. We obtain reliable estimates for Dirichlet and acoustic boundary conditions…
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 saddle point problems which objective functions are the average of $n$ strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence…
This paper introduces a preconditioned method designed to comprehensively address the saddle point system with the aim of improving convergence efficiency. In the preprocessor construction phase, a technical approach for solving the…
In this work, we present a POD-greedy reduced basis method for parabolic partial differential equations (PDEs), based on the least squares space-time formulation proposed in [Hinze, Kahle, Stahl, A least-squares space-time approach for…
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…
Recently, in (M. Masoudi, D.K. Salkuyeh, An extension of positive-definite and skew-Hermitian splitting method for preconditioning of generalized saddle point problems, Computers \& Mathematics with Application,…
We analyze a pointwise tracking multiobjective optimal control problem subject to the Poisson problem and bilateral control constraints. To approximate Pareto optimal points and the Pareto front numerically, we consider two different finite…
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…
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…
The constrained minimization (respectively maximization) of directed distances and of related generalized entropies is a fundamental task in information theory as well as in the adjacent fields of statistics, machine learning, artificial…
This paper studies the generalization bounds for the empirical saddle point (ESP) solution to stochastic saddle point (SSP) problems. For SSP with Lipschitz continuous and strongly convex-strongly concave objective functions, we establish…
We present a reduced basis approach to solve the convected Helmholtz equation with several physical parameters. Physical parameters characterize the aeroacoustic wave propagation in terms of the wave and Mach numbers. We compute solutions…
A posteriori error analysis is a technique to quantify the error in particular simulations of a numerical approximation method. In this article, we use such an approach to analyze how various error components propagate in certain moving…
Reduced order models, in particular the reduced basis method, rely on empirically built and problem dependent basis functions that are constructed during an off-line stage. In the on-line stage, the precomputed problem-dependent solution…
We propose an a posteriori error estimator for a sparse optimal control problem: the control variable lies in the space of regular Borel measures. We consider a solution technique that relies on the discretization of the control variable as…
In this paper we present a simple method of deriving a posteriori error equalities and estimates for linear elliptic and parabolic partial differential equations. The error is measured in a combined norm taking into account both the primal…