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In this paper we introduce and analyze the residual-based a posteriori error estimation of the partially penalized immersed finite element method for solving elliptic interface problems. The immersed finite element method can be naturally…

Numerical Analysis · Mathematics 2019-10-18 Cuiyu He , Xu Zhang

The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…

Numerical Analysis · Mathematics 2022-02-25 Qichen Hong , Hehu Xie , Fei Xu

In this paper, we introduce a new finite element method for solving the Stokes equations in the primary velocity-pressure formulation. This method employs $H(div)$ finite elements to approximate velocity, which leads to two unique…

Numerical Analysis · Mathematics 2020-06-23 Xiu Ye , Shangyou Zhang

This paper introduces a discretization-accurate stopping criterion of symmetric iterative methods for solving systems of algebraic equations resulting from the finite element approximation. The stopping criterion consists of the evaluations…

Numerical Analysis · Mathematics 2019-09-19 Zhiqiang Cai , Shuhao Cao , Robert D. Falgout

We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…

Optimization and Control · Mathematics 2025-05-08 Francisco Fuica , Nicolai Jork

This paper introduces a novel a posteriori error estimation framework for the enriched Galerkin (EG) finite element method applied to linear parabolic equations. While the EG method has been recognized for its local conservation property…

Numerical Analysis · Mathematics 2026-04-29 Hyun-Geun Shin , Yi-Yung Yang , Sanghyun Lee

This paper addresses the problem of evaluating the quality of finite element meshes for the purpose of structural mechanic simulations. It proposes the application of a machine learning model trained on data collected from expert…

Machine Learning · Computer Science 2021-07-23 Joachim Sprave , Christian Drescher

This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique…

Numerical Analysis · Computer Science 2011-07-20 Stephane PA Bordas , Sundararajan Natarajan

Efficient structural reanalysis for high-rank modification plays an important role in engineering computations which require repeated evaluations of structural responses, such as structural optimization and probabilistic analysis. To…

Computational Engineering, Finance, and Science · Computer Science 2025-05-20 Wenxiong Li , Suiyin Chen , Huan Huang

Finite element plate and shell formulations are ubiquitous in structural analysis for modeling all kinds of slender structures, both for static and dynamic analyses. The latter are particularly challenging as the high order nature of the…

Numerical Analysis · Mathematics 2025-09-03 Giuliano Guarino , Yannis Voet , Pablo Antolin , Annalisa Buffa

The efficient and reliable approximation of convection-dominated problems continues to remain a challenging task. To overcome the difficulties associated with the discretization of convection-dominated equations, stabilization techniques…

Numerical Analysis · Mathematics 2022-12-15 Marius Paul Bruchhäuser , Kristina Schwegler , Markus Bause

In computational engineering, ensuring the integrity and safety of structures in fields such as aerospace and civil engineering relies on accurate stress prediction. However, analytical methods are limited to simple test cases, and…

Computational Engineering, Finance, and Science · Computer Science 2025-10-31 Fabian Key , Lukas Freinberger

In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…

Systems and Control · Computer Science 2016-08-09 Laurent Bako , Henrik Ohlsson

We derive optimal order a posteriori error estimates for fully discrete approximations of linear Schr\"odinger-type equations, in the $L^\infty(L^2)-$norm. For the discretization in time we use the Crank-Nicolson method, while for the space…

Numerical Analysis · Mathematics 2013-04-10 Theodoros Katsaounis , Irene Kyza

This paper presents a pressure-robust discretizations, specifically within the context of optimal control problems for the Stokes-Darcy system. The study meticulously revisits the formulation of the divergence constraint and the enforcement…

Numerical Analysis · Mathematics 2025-02-25 Jingshi Li , Jiachuan Zhang , Ran Zhang

This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…

Numerical Analysis · Mathematics 2026-03-27 Stefan Frei , Tobias Knoke , Marc C. Steinbach , Anne-Kathrin Wenske , Thomas Wick

We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…

Optimization and Control · Mathematics 2024-04-12 Yutong Dai , Xiaoyi Qu , Daniel P. Robinson

In this paper, an error analysis of a three steps two level Galekin finite element method for the two dimensional transient Navier-Stokes equations is discussed. First of all, the problem is discretized in spatial direction by employing…

Numerical Analysis · Mathematics 2014-01-23 Saumya Bajpai , Amiya K. Pani

This short communication discusses two alternate techniques to treat hanging nodes in a quadtree mesh. Both the techniques share similarities, in that, they require only boundary information. Moreover, they do not require an explicit form…

Numerical Analysis · Mathematics 2013-10-17 Sundararajan Natarajan , Ean Tat Ooi , Hou Man , Chongmin Song

We present the Neural Approximated Virtual Element Method to numerically solve elasticity problems. This hybrid technique combines classical concepts from the Finite Element Method and the Virtual Element Method with recent advances in deep…

Numerical Analysis · Mathematics 2025-07-09 Stefano Berrone , Moreno Pintore , Gioana Teora