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We consider a control-constrained optimal control problem subject to time-harmonic Maxwell's equations; the control variable belongs to a finite-dimensional set and enters the state equation as a coefficient. We derive existence of optimal…

Numerical Analysis · Mathematics 2024-05-10 Francisco Fuica , Felipe Lepe , Pablo Venegas

This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind…

Numerical Analysis · Mathematics 2026-02-04 Lutz Angermann

We consider inverse problems estimating distributed parameters from indirect noisy observations through discretization of continuum models described by partial differential or integral equations. It is well understood that the errors…

Numerical Analysis · Mathematics 2023-10-09 Albero Bocchinfuso , Daniela Calvetti , Erkki Somersalo

Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…

Numerical Analysis · Mathematics 2015-02-02 Vishwas Rao , Adrian Sandu

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 element based adaptation method is developed for an anisotropic a posteriori error estimator. The adaptation does not make use of a metric, but instead equidistributes the error over elements using local mesh modifications. Numerical…

Numerical Analysis · Mathematics 2016-12-20 Edward Boey , Yves Bourgault , Thierry Giordano

We propose and analyze a posteriori error estimates for a control-constrained optimal control problem with bang-bang solutions. We consider a solution strategy based on the variational approach, where the control variable is not…

Optimization and Control · Mathematics 2025-05-26 Francisco Fuica

Adaptive control provides techniques for adjusting control parameters in real time to maintain system performance despite unknown or changing process parameters. These methods use real data to tune controllers and adjust plant models or…

Systems and Control · Electrical Eng. & Systems 2024-06-12 Ioan Doré Landau , Rogelio Lozano , Mohammed M Saad , Alireza Karimi

This work is focused on the application of functional-type a posteriori error estimates and corresponding indicators to a class of time-dependent problems. We consider the algorithmic part of their derivation and implementation and also…

Numerical Analysis · Computer Science 2017-05-25 Bärbel Holm , Svetlana Matculevich

In this work, we consider adaptive mesh refinement for a monolithic phase-field description for fractures in brittle materials. Our approach is based on an a posteriori error estimator for the phase-field variational inequality realizing…

Numerical Analysis · Mathematics 2019-10-03 Katrin Mang , Mirjam Walloth , Thomas Wick , Winnifried Wollner

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical…

Numerical Analysis · Computer Science 2015-06-22 John D. Jakeman , Timothy Wildey

An posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies on very general polygonal/polyhedral meshes. The estimator is…

Numerical Analysis · Mathematics 2017-04-26 Andrea Cangiani , Emmanuil H. Georgoulis , Tristan Pryer , Oliver J. Sutton

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

For the first time we introduce an error estimator for the numerical approximation of the equations describing the dynamics of sea ice. The idea of the estimator is to identify different error contributions coming from spatial and temporal…

Numerical Analysis · Mathematics 2020-08-11 Carolin Mehlmann , Thomas Richter

We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…

Numerical Analysis · Mathematics 2019-01-14 Alejandro Allendes , Francisco Fuica , Enrique Otárola

We develop a novel a posteriori error estimator for the $L^2$ error committed by the finite element discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi-discretization…

Numerical Analysis · Mathematics 2023-03-14 Raphaël Bulle , Olga Barrera , Stéphane P. A. Bordas , Franz Chouly , Jack S. Hale

As we look to the next generation of adaptive optics systems, now is the time to develop and explore the technologies that will allow us to image rocky Earth-like planets; wavefront control algorithms are not only a crucial component of…

Earth and Planetary Astrophysics · Physics 2023-09-06 J. Fowler , Rico Landman

The binary Mumford-Shah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision, ranging from basic segmentation and labeling to…

Numerical Analysis · Mathematics 2015-05-21 Benjamin Berkels , Alexander Effland , Martin Rumpf

In this paper, we give a new type of a posteriori error estimators suitable for moving finite element methods under anisotropic meshes for general second-order elliptic problems. The computation of estimators is simple once corresponding…

Numerical Analysis · Mathematics 2015-03-17 Xiaobo Yin , Hehu Xie

This paper develops some extensions to the work of [1] which studied the continuous-time adaptive output tracking control schemes with the reference output signal generated from an unknown reference model system. The presented extensions…

Systems and Control · Electrical Eng. & Systems 2024-12-17 Gang Tao