Related papers: Error estimation and uncertainty quantification fo…
Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…
For the finite element solution of Poisson's equation, a local a posteriori error estimation based on the Hypercircle method is proposed. Even for the solution of Poisson's equation without the $H^2$ regularity, this method can provide…
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…
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…
We establish guaranteed and practically computable a posteriori error bounds for source problems and eigenvalue problems involving linear Schr{\"o}dinger operators with atom-centered potentials discretized with linear combinations of atomic…
Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…
A posteriori error estimators are studied for discontinuous Galerkin methods for solving a frictional contact problem, which is a representative elliptic variational inequality of the second kind. The estimators are derived by relating the…
Using instruments comprising ordered responses to items are ubiquitous for studying many constructs of interest. However, using such an item response format may lead to items with response categories infrequently endorsed or unendorsed…
We propose a simple approach that provides accurate uncertainty quantification for Bayesian inference in misspecified or approximate models, and for generalized (Gibbs) posteriors. While existing solutions in this context are based on…
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…
We propose a method of obtaining a posteriori estimates which does not use the duality theory and which applies to variational inequalities with monotone operators, without assuming the potentiality of operators. The effectiveness of the…
This work develops user-friendly a posteriori error estimates of finite element methods, based on smoothers of linear iterative solvers. The proposed method employs simple smoothers, such as Jacobi or Gauss-Seidel iteration, on an auxiliary…
There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…
It has recently been established that the numerical solution of ordinary differential equations can be posed as a nonlinear Bayesian inference problem, which can be approximately solved via Gaussian filtering and smoothing, whenever a…
We present the first systematic work for deriving a posteriori error estimates for general non-polynomial basis functions in an interior penalty discontinuous Galerkin (DG) formulation for solving eigenvalue problems associated with second…
Previous results pertaining to algebraic state and parameter estimation of linear systems based on a special construction of a forward-backward kernel representation of linear differential invariants are extended to handle large noise in…
In this paper we show that the classical problem of frequency estimation can be formulated and solved efficiently in an empirical Bayesian framework by assigning a uniform a priori probability distribution to the unknown frequency. We…
For the numerical solution of the American option valuation problem, we provide a script written in MATLAB implementing an explicit finite difference scheme. Our main contribute is the definition of a posteriori error estimator for the…
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…
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…