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We propose and analyze a reliable and efficient a posteriori error estimator for a constrained linear-quadratic optimal control problem involving Dirac measures; the control variable corresponds to the amplitude of forces modeled as point…

Numerical Analysis · Mathematics 2018-10-09 Alejandro Allendes , Enrique Otarola , Richard Rankin , Abner J. Salgado

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…

Numerical Analysis · Mathematics 2018-04-05 B. Endtmayer , U. Langer , T. Wick

An integro-differential equation of hyperbolic type, with mixed boundary conditions, is considered. A continuous space-time finite element method of degree one is formulated. A posteriori error representations based on space-time cells is…

Numerical Analysis · Mathematics 2012-11-16 Fardin Saedpanah

In this work we present an a posteriori error indicator for approximation schemes of Runge-Kutta-discontinuous-Galerkin type arising in applications of compressible fluid flows. The purpose of this indicator is not only for mesh adaptivity,…

Numerical Analysis · Mathematics 2017-09-08 Jan Giesselmann , Tristan Pryer

We present an a posteriori error analysis for the mixed virtual element method (mixed VEM) applied to second order elliptic equations in divergence form with mixed boundary conditions. The resulting error estimator is of residual-type. It…

Numerical Analysis · Mathematics 2019-04-24 Andrea Cangiani , Mauricio Munar

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

A new technique of residual-type a posteriori error analysis is developed for the lowest-order Raviart-Thomas mixed finite element discretizations of convection-diffusion-reaction equations in two- or three-dimension. Both centered mixed…

Numerical Analysis · Mathematics 2015-03-26 Shaohong Du , Xiaoping Xie

In a general setting, we study a posteriori estimates used in finite element analysis to measure the error between a solution and its approximation. The latter is not necessarily generated by a finite element method. We show that the error…

Numerical Analysis · Mathematics 2025-07-09 Thomas Führer , Sergio Rojas

We derive a residual-based a posteriori error estimator for the conforming hp-Adaptive Finite Element Method (hp-AFEM) for the steady state Stokes problem describing the slow motion of an incompressible fluid. This error estimator is…

Numerical Analysis · Mathematics 2021-02-16 Arezou Ghesmati , Wolfgang Bangerth , Bruno Turcksin

Defeaturing, the process of simplifying computational geometries, is a critical step in industrial simulation pipelines for reducing computational cost. Rigorous a posteriori estimators exist for the global energy-norm error introduced by…

Numerical Analysis · Mathematics 2025-12-24 Philipp Weder , Annalisa Buffa

In this paper, we propose a novel approximation strategy for time-dependent hyperbolic systems of conservation laws for the Euler system of gas dynamics that aims to represent the dynamics of strong interacting discontinuities. The goal of…

Numerical Analysis · Mathematics 2023-01-16 Paola Bacigaluppi , Rémi Abgrall , Svetlana Tokareva

We present a priori and a posteriori error analysis of a Virtual Element Method (VEM) to approximate the vibration frequencies and modes of an elastic solid. We analyze a variational formulation relying only on the solid displacement and…

Numerical Analysis · Mathematics 2017-12-20 David Mora , Gonzalo Rivera

In this article we develop function-based a posteriori error estimators for the solution of linear second order elliptic problems considering hierarchical spline spaces for the Galerkin discretization. We prove a global upper bound for the…

Numerical Analysis · Mathematics 2016-11-24 Annalisa Buffa , Eduardo M. Garau

We propose a randomized a posteriori error estimator for reduced order approximations of parametrized (partial) differential equations. The error estimator has several important properties: the effectivity is close to unity with prescribed…

Numerical Analysis · Mathematics 2019-04-02 Kathrin Smetana , Olivier Zahm , Anthony T Patera

This paper proposes a nonlinear estimator for the robust reconstruction of process and sensor faults for a class of uncertain nonlinear systems. The proposed fault estimation method augments the system dynamics with an ultra-local (in time)…

Systems and Control · Electrical Eng. & Systems 2024-06-11 Farhad Ghanipoor , Carlos Murguia , Peyman Mohajerin Esfahani , Nathan van de Wouw

We consider so-called Herrmann and Hydrostatic mixed formulations of classical linear elasticity and analyse the error associated with locally stabilised $P_1-P_0$ finite element approximation. First, we prove a stability estimate for the…

Numerical Analysis · Mathematics 2018-01-15 Arbaz Khan , Catherine E. Powell , David J. Silvester

We propose new a posteriori error estimators for non-conforming finite element discretizations of second-order elliptic PDE problems. These estimators are based on novel reformulations of the standard Prager-Synge identity, and enable to…

Numerical Analysis · Mathematics 2026-01-22 T. Chaumont-Frelet

We present a fully computable a posteriori error estimator for piecewise linear finite element approximations of reaction-diffusion problems with mixed boundary conditions and piecewise constant reaction coefficient formulated in arbitrary…

Numerical Analysis · Mathematics 2015-07-06 Mark Ainsworth , Tomáš Vejchodský

This work presents the multiharmonic analysis and derivation of functional type a posteriori estimates of a distributed eddy current optimal control problem and its state equation in a time-periodic setting. The existence and uniqueness of…

Optimization and Control · Mathematics 2023-08-10 Monika Wolfmayr

We consider a linear elliptic partial differential equation (PDE) with a generic uniformly bounded parametric coefficient. The solution to this PDE problem is approximated in the framework of stochastic Galerkin finite element methods. We…

Numerical Analysis · Mathematics 2020-06-05 Alex Bespalov , Feng Xu