English
Related papers

Related papers: Multigoal-oriented error estimation and mesh adapt…

200 papers

In this paper we consider optimal control of nonlinear time-dependent fluid structure interactions. To determine a time-dependent control variable a BFGS algorithm is used, whereby gradient information is computed via a dual problem. To…

Optimization and Control · Mathematics 2020-08-11 L. Failer , T. Richter

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

In this work, we derive two-sided a posteriori error estimates for the dual-weighted residual (DWR) method. We consider both single and multiple goal functionals. Using a saturation assumption, we derive lower bounds yielding the efficiency…

Numerical Analysis · Mathematics 2018-11-20 Bernhard Endtmayer , Ulrich Langer , Thomas Wick

A posteriori estimates give bounds on the error between the unknown solution of a partial differential equation and its numerical approximation. We present here the methodology based on H1-conforming potential and H(div)-conforming…

Numerical Analysis · Mathematics 2025-05-30 Martin Vohralík , Soleiman Yousef

In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…

Numerical Analysis · Mathematics 2014-04-24 Michael Holst , Sara Pollock , Yunrong Zhu

Topology optimization methods face serious challenges when applied to structural design with fluid-structure interaction (FSI) loads, specially for high Reynolds fluid flow. This paper devises an explicit boundary method that employs…

In this work, a multirate in time approach resolving the different time scales of a convection-dominated transport and coupled fluid flow is developed and studied in view of goal-oriented error control by means of the Dual Weighted Residual…

Numerical Analysis · Mathematics 2022-12-09 Marius Paul Bruchhäuser , Uwe Köcher , Markus Bause

We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…

Numerical Analysis · Mathematics 2017-08-03 Alejandro Allendes , Enrique Otarola , Richard Rankin

The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…

Numerical Analysis · Mathematics 2022-02-11 Vladimír Lukeš , Eduard Rohan

A mixed continuous / discontinuous Galerkin scheme is introduced for the simulation of fluid-structure interaction problems in an isogeometric analysis framework. The properties of Non-Uniform Rational B-Spline basis functions are leveraged…

Analysis of PDEs · Mathematics 2026-02-17 Régis Duvigneau

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

We present a scheme implementing an a posteriori refinement strategy in the context of a high-order meshless method for problems involving point singularities and fluid-solid interfaces. The generalized moving least squares (GMLS)…

Computational Physics · Physics 2019-07-24 Wei Hu , Nathaniel Trask , Xiaozhe Hu , Wenxiao Pan

The known a posteriori error analysis of hybrid high-order methods (HHO) treats the stabilization contribution as part of the error and as part of the error estimator for an efficient and reliable error control. This paper circumvents the…

Numerical Analysis · Mathematics 2024-07-03 Fleurianne Bertrand , Carsten Carstensen , Benedikt Gräßle , Ngoc Tien Tran

We consider an adaptive finite element method with arbitrary but fixed polynomial degree $p \ge 1$, where adaptivity is driven by an edge-based residual error estimator. Based on the modified maximum criterion from [Diening et al, Found.…

Numerical Analysis · Mathematics 2021-01-29 Michael Innerberger , Dirk Praetorius

A defect-deferred correction method, increasing both temporal and spatial accuracy, for fluid-fluid interaction problem with nonlinear interface condition is considered by geometric averaging of the previous two-time levels. In the defect…

Numerical Analysis · Mathematics 2020-06-02 Mustafa Aggul , Songül Kaya

There is a wide range of stabilized finite element methods for stationary and non-stationary convection-diffusion equations such as streamline diffusion methods, local projection schemes, subgrid-scale techniques, and continuous interior…

Numerical Analysis · Mathematics 2014-02-25 L. Tobiska , R. Verfürth

Multi-objective optimization is central to many engineering and machine learning applications, where multiple objectives must be optimized in balance. While multi-gradient based optimization methods combine these objectives in each step,…

Optimization and Control · Mathematics 2026-05-13 Trang H. Tran , Luis Nunes Vicente

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 consider the unilateral contact problem between an elastic body and a rigid foundation in a description that includes both Tresca and Coulomb friction conditions. For this problem, we present an a posteriori error analysis based on an…

Numerical Analysis · Mathematics 2024-01-08 Ilaria Fontana , Daniele A. Di Pietro

This article presents a Galerkin projection-based reduced-order modelling (ROM) approach for segregated fluid-structure interaction (FSI) problems, formulated within an Arbitrary Lagrangian Eulerian (ALE) framework at low Reynolds numbers…

Numerical Analysis · Mathematics 2025-07-24 Valentin Nkana Ngan , Giovanni Stabile , Andrea Mola , Gianluigi Rozza