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There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often…

Methodology · Statistics 2022-11-07 Euan T. McGonigle , Haeran Cho

Based on the auxiliary subspace techniques, a hierarchical basis a posteriori error estimator is proposed for the Stokes problem in two and three dimensions. For the error estimator, we need to solve only two global diagonal linear systems…

Numerical Analysis · Mathematics 2023-03-22 Jiachuan Zhang , Ran Zhang , Xiaoshen Wang

The computation time required by standard finite difference methods with fixed timesteps for solving fractional diffusion equations is usually very large because the number of operations required to find the solution scales as the square of…

Numerical Analysis · Mathematics 2024-06-28 Santos B. Yuste , Joaquin Quintana-Murillo

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…

Numerical Analysis · Mathematics 2025-05-06 Ramon Codina , Hauke Gravenkamp , Sheraz Ahmed Khan

We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…

Numerical Analysis · Mathematics 2015-06-22 A. Johansson , J. H. Chaudry , V. Carey , D. Estep , V. Ginting , M. Larson , S. Tavener

Generalized method of moments estimators based on higher-order moment conditions derived from independent shocks can be used to identify and estimate the simultaneous interaction in structural vector autoregressions. This study highlights…

Econometrics · Economics 2023-10-13 Sascha A. Keweloh

A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The strategy extends the a posteriori error estimation framework introduced by Guignard and…

Numerical Analysis · Mathematics 2022-02-21 Alex Bespalov , David J. Silvester

This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control…

Numerical Analysis · Mathematics 2020-05-13 Wayne Isaac Tan Uy , Benjamin Peherstorfer

We propose and analyze a reliable and efficient a posteriori error estimator for the pointwise tracking optimal control problem of the Stokes equations. This linear-quadratic optimal control problem entails the minimization of a cost…

Numerical Analysis · Mathematics 2018-10-08 Alejandro Allendes , Francisco Fuica , Enrique Otárola , Daniel Quero

This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational…

Numerical Analysis · Mathematics 2007-05-23 E. Mordecki , A. Szepessy , R. Tempone , G. E. Zouraris

We consider the a posteriori error estimation for an atomistic-to-continuum cou- pling scheme for a generic one-dimensional many-body next-nearest-neighbour interaction model in 1D. We derive and rigorously prove the efficiency of the…

Numerical Analysis · Mathematics 2017-02-27 Hao Wang , Siyao Yang

This work proposes an adaptive framework to solve a robust structural shape optimization problem governed by linear elasticity models that account for uncertainties in the loading and material inputs. A posteriori error estimators are…

Optimization and Control · Mathematics 2026-02-06 Oğuz Han Altıntaş , Hamdullah Yücel

This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…

Numerical Analysis · Mathematics 2012-04-10 Stéphane Descombes , Max Duarte , Thierry Dumont , Violaine Louvet , Marc Massot

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…

Numerical Analysis · Mathematics 2018-03-20 Kristina Schwegler , Marius P. Bruchhäuser , Markus Bause

Time delay estimation plays a critical role in control, stabilization and state estimation of many practical system with time delay. In this paper, we propose a method to estimate delay for discrete time linear multiple-input…

Systems and Control · Electrical Eng. & Systems 2021-09-08 Iman Shafikhani , Hazhar Sufi Karimi , Mohammad Mohammadian , Amin Ramezani , Hamid Reza Momeni

A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems of Dirichlet and mixed boundary conditions are proposed. Stability and efficiency of the estimators are proved. Finally, we provide…

Numerical Analysis · Mathematics 2017-05-12 Long Chen , Jun Hu , Xuehai Huang , Hongying Man

We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…

Numerical Analysis · Mathematics 2026-04-24 Zhaonan Dong , Emmanuil H. Georgoulis , Lorenzo Mascotto , Zuodong Wang

We consider Poisson's equation with a finite number of weighted Dirac masses as a source term, together with its discretization by means of conforming finite elements. For the error in fractional Sobolev spaces, we propose residual-type a…

Numerical Analysis · Mathematics 2015-07-30 Fernando D. Gaspoz , Pedro Morin , Andreas Veeser

This paper introduces a new computational methodology for determining a-posteriori multi-objective error estimates for finite-element approximations, and for constructing corresponding (quasi-)optimal adaptive refinements of finite-element…

Numerical Analysis · Mathematics 2016-11-23 E. H. van Brummelen , S. Zhuk , G. J. van Zwieten

We introduce a dynamic approach to probabilistic forecast reconciliation at scale. Our model differs from the existing literature in this area in several important ways. Firstly we explicitly allow the weights allocated to the base…

Methodology · Statistics 2024-09-20 Ross Hollyman , Fotios Petropoulos , Michael E. Tipping