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This paper studies the problem of parameter estimation in resonant, acoustic fluid-structure interaction problems over a wide frequency range. Problems with multiple resonances are known to be subjected to local minima, which represents a…

Computational Physics · Physics 2019-03-06 Peter Göransson , Jacques Cuenca , Timo Lähivaara

We consider the approximation of singularly perturbed linear second-order boundary value problems by $hp$-finite element methods. In particular, we include the case where the associated differential operator may not be coercive. Within this…

Numerical Analysis · Mathematics 2015-04-30 Jens M. Melenk , Thomas P. Wihler

This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic solid is almost incompressible. Several novel a posteriori…

Numerical Analysis · Mathematics 2018-06-15 Arbaz Khan , Catherine E. Powell , David J. Silvester

This work deals with the a posteriori error estimates for the Darcy-Forchheimer problem. We introduce the corresponding variational formulation and discretize it by using the finite-element method. A posteriori error estimate with two types…

Numerical Analysis · Mathematics 2022-02-24 Georges Semaan , Toni Sayah , Faouzi Triki

We propose and analyze an a posteriori error estimator for a PDE-constrained optimization problem involving a nondifferentiable cost functional, fractional diffusion, and control-constraints. We realize fractional diffusion as the…

Numerical Analysis · Mathematics 2019-06-04 Enrique Otarola

We show how a posteriori goal oriented error estimation can be used to efficiently solve the subproblems occurring in a Model Predictive Control (MPC) algorithm. In MPC, only an initial part of a computed solution is implemented as a…

Optimization and Control · Mathematics 2022-03-02 Lars Grüne , Manuel Schaller , Anton Schiela

This article is a review on basic concepts and tools devoted to a posteriori error estimation for problems solved with the Finite Element Method. For the sake of simplicity and clarity, we mostly focus on linear elliptic diffusion problems,…

Numerical Analysis · Mathematics 2021-10-06 Ludovic Chamoin , Frederic Legoll

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

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…

Numerical Analysis · Mathematics 2022-01-12 Felipe Lepe , Gonzalo Rivera , Jesús Vellojín

We introduce novel a posteriori error indicators for a nonlinear least-squares solver for smooth solutions of the Monge--Amp\`ere equation on convex polygonal domains in $\mathbb{R}^2$. At each iteration, our iterative scheme decouples the…

Numerical Analysis · Mathematics 2025-09-09 Alexandre Caboussat , Anna Peruso , Marco Picasso

We consider finite element discretizations of Maxwell's equations coupled with a non-local hydrodynamic Drude model that accurately accounts for electron motions in metallic nanostructures. Specifically, we focus on a posteriori error…

Numerical Analysis · Mathematics 2021-08-04 T. Chaumont-Frelet , S. Lanteri , P. Vega

We provide a posteriori error estimates in the energy norm for temporal semi-discretisations of wave maps into spheres that are based on the angular momentum formulation. Our analysis is based on novel weak-strong stability estimates which…

Numerical Analysis · Mathematics 2023-07-25 Jan Giesselmann , Elena Mäder-Baumdicker , David Jakob Stonner

We consider second-order PDE problems set in unbounded domains and discretized by Lagrange finite elements on a finite mesh, thus introducing an artificial boundary in the discretization. Specifically, we consider the reaction diffusion…

Numerical Analysis · Mathematics 2025-03-31 T. Chaumont-Frelet

In the present work, we derive functional upper bounds for the potential error arising from finite-element boundary-element coupling formulations for a nonlinear Poisson-type transmission problem. The proposed a posteriori error estimates…

Numerical Analysis · Mathematics 2026-02-17 Alexander Freiszlinger , Dirk Pauly , Dirk Praetorius , Michael Schomburg

In this paper, we study the "a posteriori" error estimate corresponding to the Brinkman-Darcy-Forchheimer problem. We introduce the variational formulation discretised by using the finite element method. Then, we establish an "a posteriori"…

Numerical Analysis · Mathematics 2021-04-29 Toni Sayah

This paper focuses on a posteriori error estimates for a pressure-robust finite element method, which incorporates a divergence-free reconstruction operator, within the context of the distributed optimal control problem constrained by the…

Numerical Analysis · Mathematics 2026-01-30 Jingshi Li , Jiachuan Zhang

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

System level synthesis enables improved robust MPC formulations by allowing for joint optimization of the nominal trajectory and controller. This paper introduces a tailored algorithm for solving the corresponding disturbance feedback…

Optimization and Control · Mathematics 2024-09-05 Antoine P. Leeman , Johannes Köhler , Florian Messerer , Amon Lahr , Moritz Diehl , Melanie N. Zeilinger

A general framework for goal-oriented a posteriori error estimation for finite volume methods is presented. The framework does not rely on recasting finite volume methods as special cases of finite element methods, but instead directly…

Numerical Analysis · Mathematics 2011-08-24 Qingshan Chen , Max Gunzburger

Scientists and engineers are often interested in learning the number of subpopulations (or components) present in a data set. A common suggestion is to use a finite mixture model (FMM) with a prior on the number of components. Past work has…

Statistics Theory · Mathematics 2021-07-08 Diana Cai , Trevor Campbell , Tamara Broderick