相关论文: An a posteriori error estimate of the outer normal…

In a previous work, we introduced a discretization scheme for a constrained optimal control problem involving the fractional Laplacian. For such a control problem, we derived optimal a priori error estimates that demand the convexity of the…

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…

This paper derives a posteriori error estimates for the mixed numerical approximation of the Laplace eigenvalue problem with homogeneous Dirichlet boundary conditions. In particular, the resulting error estimator constitutes an upper bound…

This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…

Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…

Residual-based a~posteriori error estimators are derived for the modified Morley FEM, proposed by Wang, Xu, Hu [J. Comput. Math, 24(2), 2006], for the singularly perturbed biharmonic equation and the nonlinear von K\'arm\'an equations. The…

This work studies a posteriori error estimates and their use for time-dependent acoustic scattering problems, formulated as a time-dependent boundary integral equation based on a single-layer ansatz. The integral equation is discretized by…

In this work, we further develop multigoal-oriented a posteriori error estimation with two objectives in mind. First, we formulate goal-oriented mesh adaptivity for multiple functionals of interest for nonlinear problems in which both the…

In this paper, we introduce a novel a posteriori error estimator for the conforming finite element approximation to the H(curl) problem with inhomogeneous media and with the right-hand side only in L^2. The estimator is of the recovery…

The issue of single-grid discretization error estimator, operating in the postprocessor mode, is addressed in the paper. An ensemble of numerical solutions, obtained using solvers of different accuracy, is shown to provide an upper estimate…

We propose a Bayesian approach using improper priors for hierarchical linear mixed models with flexible random effects and residual error distributions. The error distribution is modelled using scale mixtures of normals, which can capture…

Probabilistic modeling is cyclical: we specify a model, infer its posterior, and evaluate its performance. Evaluation drives the cycle, as we revise our model based on how it performs. This requires a metric. Traditionally, predictive…

The spectral deferred correction method is a variant of the deferred correction method for solving ordinary differential equations. A benefit of this method is that is uses low order schemes iteratively to produce a high order…

Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

In this paper, we propose a general approach for explicit a posteriori error representation for convex minimization problems using basic convex duality relations. Exploiting discrete orthogonality relations in the space of element-wise…

We prove quasi-optimal a priori error estimates for finite element approximations of boundary normal fluxes in the $L^2$-norm. Our results are valid for a variety of different schemes for weakly enforcing Dirichlet boundary conditions…

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 extend the approximate residual balancing (ARB) framework to nonlinear models, answering an open problem posed by Athey et al. (2018). Our approach addresses the challenge of estimating average treatment effects in high-dimensional…

Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference…