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Related papers: Robust topology optimization using a posteriori er…

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We present a posteriori error analysis in the supremum norm for the symmetric interior penalty discontinuous Galerkin method for the elliptic obstacle problem. We construct discrete barrier functions based on appropriate corrections of the…

Numerical Analysis · Mathematics 2021-08-27 Blanca Ayuso de Dios , Thirupathi Gudi , Kamana Porwal

Classical gradient-based density topology optimization is adapted for method-of-moments numerical modeling to design a conductor-based system attaining the minimal antenna Q-factor evaluated via an energy stored operator. Standard topology…

Optimization and Control · Mathematics 2023-12-22 Jonas Tucek , Miloslav Capek , Lukas Jelinek , Ole Sigmund

Multilevel methods represent a powerful approach in numerical solution of partial differential equations. The multilevel structure can also be used to construct estimates for total and algebraic errors of computed approximations. This paper…

Numerical Analysis · Mathematics 2024-05-13 Petr Vacek , Jan Papež , Zdeněk Strakoš

We propose a posteriori error estimators for classical low-order inf-sup stable and stabilized finite element approximations of the Stokes problem with singular sources in two and three dimensional Lipschitz, but not necessarily convex,…

Numerical Analysis · Mathematics 2019-01-30 Alejandro Allendes , Enrique Otarola , Abner J. Salgado

We present a hybrid a-priori/a-posteriori goal oriented error estimator for a combination of dynamic iteration-based solution of ordinary differential equations discretized by finite elements. Our novel error estimator combines estimates…

Numerical Analysis · Mathematics 2026-02-13 Erik Weyl , Andreas Bartel , Manuel Schaller

We present a finite-difference method for the topology optimization of permanent magnets that is based on the FFT accelerated computation of the stray-field. The presented method employs the density approach for topology optimization and…

Computational Physics · Physics 2017-10-11 Claas Abert , Christian Huber , Florian Bruckner , Christoph Vogler , Gregor Wautischer , Dieter Suess

A class of linear parabolic equations are considered. We give a posteriori error estimates in the maximum norm for a method that comprises extrapolation applied to the backward Euler method in time and finite element discretisations in…

Numerical Analysis · Mathematics 2022-08-18 Torsten Linß , Goran Radojev

We consider the Virtual Element method (VEM) introduced by Beir\~ao da Veiga, Lovadina and Vacca in 2016 for the numerical solution of the steady, incompressible Navier-Stokes equations; the method has arbitrary order $k \geq 2$ and…

Numerical Analysis · Mathematics 2023-01-02 Claudio Canuto , Davide Rosso

In this work we develop an a posteriori error analysis of a conforming mixed finite element method for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium on isotropic meshes in…

Numerical Analysis · Mathematics 2020-04-23 Koffi Wilfrid Houédanou

Time-fractional parabolic equations with a Caputo time derivative are considered. For such equations, we explore and further develop the new methodology of the a-posteriori error estimation and adaptive time stepping proposed in [7]. We…

Numerical Analysis · Mathematics 2023-01-27 Sebastian Franz , Natalia Kopteva

We describe a posteriori error analysis for a discontinuous Galerkin method for a fourth order elliptic interface problem that arises from a linearized model of thin sheet folding. The primary contribution is a local efficiency bound for an…

Numerical Analysis · Mathematics 2025-07-02 Harbir Antil , Sean P. Carney , Rohit Khandelwal

A priori and a posteriori error analysis of $hp$ finite element method for elliptic control problem with Robin boundary condition and boundary observation are presented. are presented. Through the Cl\'ement-type approach and the…

Numerical Analysis · Mathematics 2026-01-29 Xingyuan Lin , Xiuxiu Lin , Xuesong Chen

A class of linear parabolic equations is considered. We derive a framework for the a posteriori error analysis of time discretisations by Richardson extrapolation of arbitrary order combined with finite element discretisations in space. We…

Numerical Analysis · Mathematics 2024-11-22 Torsten Linß , Goran Radojev

We develop all of the components needed to construct an adaptive finite element code that can be used to approximate fractional partial differential equations, on non-trivial domains in $d\geq 1$ dimensions. Our main approach consists of…

Numerical Analysis · Mathematics 2018-02-14 Mark Ainsworth , Christian Glusa

In this paper, the a posteriori error estimates of the exponential midpoint method for time discretization are studied for linear and semilinear parabolic equations. Using the exponential midpoint approximation defined by a continuous and…

Numerical Analysis · Mathematics 2024-06-13 Xianfa Hu , Wansheng Wang , Mengli Mao , Jiliang Cao

We propose a new algorithm for the solution of the robust multiple-load topology optimization problem. The algorithm can be applied to any type of problem, e.g., truss topology, variable thickness sheet or free material optimization. We…

Optimization and Control · Mathematics 2013-07-30 Michal Kocvara

A posteriori error estimates are derived in the context of two-dimensional structural elastic shape optimization under the compliance objective. It is known that the optimal shape features are microstructures that can be constructed using…

Numerical Analysis · Mathematics 2015-01-30 Benedict Geihe , Martin Rumpf

A residual based {\em a posteriori} error estimator is derived for a quadratic finite element method (fem) for the elliptic obstacle problem. The error estimator involves various residuals consisting the data of the problem, discrete…

Numerical Analysis · Mathematics 2014-04-14 Thirupathi Gudi , Kamana Porwal

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

In this work, we propose an a pointwise a posteriori error estimator for conforming finite element approximations of eigenfunctions corresponding to multiple and clustered eigenvalues of elliptic operators. It is proven that the pointwise a…

Numerical Analysis · Mathematics 2025-11-12 Zhenglei Li , Qigang Liang , Xuejun Xu