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This paper presents a quasi-monolithic localized high-order arbitrary Lagrangian-Eulerian (qMLH-ALE) finite element method for multi-scale fluid-structure interaction (FSI) in microfluidic systems. The fluid momentum, the incompressible…

Numerical Analysis · Mathematics 2026-05-26 Lingyue Shen , Qi Xin , Yan Chen , Jiarui Han , Yumiao Zhang , Jinchao Xu , Shihua Gong

We present a one-dimensional shear-force-driven droplet formation model with a flux-based error estimator. The model is derived using asymptotic expansion and a front-tracking method to simulate the droplet interface. The model is then…

Numerical Analysis · Mathematics 2026-05-25 Darsh Nathawani , Matthew Knepley

Multi-modal fusion of sensors is a commonly used approach to enhance the performance of odometry estimation, which is also a fundamental module for mobile robots. However, the question of \textit{how to perform fusion among different…

Robotics · Computer Science 2025-03-20 Leyuan Sun , Guanqun Ding , Yue Qiu , Yusuke Yoshiyasu , Fumio Kanehiro

This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…

Computational Engineering, Finance, and Science · Computer Science 2023-05-23 Juan F. Giraldo , Victor M. Calo

We present an anisotropic goal-oriented error estimator based on the Dual Weighted Residual (DWR) method for time-dependent convection-diffusion-reaction (CDR) equations. Using anisotropic interpolation operators the estimator is…

Numerical Analysis · Mathematics 2025-04-22 M. Bause , M. Bruchhäuser , B. Endtmayer , N. Margenberg , I. Toulopoulos , T. Wick

We introduce optimization-based full-order and reduced-order formulations of fluid structure interaction problems. We study the flow of an incompressible Newtonian fluid which interacts with an elastic body: we consider an arbitrary…

Numerical Analysis · Mathematics 2024-12-30 Tommaso Taddei , Xuejun Xu , Lei Zhang

We propose an adaptive mesh refinement strategy for immersed isogeometric analysis, with application to steady heat conduction and viscous flow problems. The proposed strategy is based on residual-based error estimation, which has been…

The prospect of assistive robots aiding in object organization has always been compelling. In an image-goal setting, the robot rearranges the current scene to match the single image captured from the goal scene. The key to an image-goal…

Robotics · Computer Science 2023-09-19 Dehao Huang , Chao Tang , Hong Zhang

The multiple-network poroelasticity (MPET) equations describe deformation and pressures in an elastic medium permeated by interacting fluid networks. In this paper, we (i) place these equations in the theoretical context of coupled…

Numerical Analysis · Mathematics 2022-11-16 Emilie Eliseussen , Marie E. Rognes , Travis B. Thompson

We consider the method of mappings for performing shape optimization for unsteady fluid-structure interaction (FSI) problems. In this work, we focus on the numerical implementation. We model the optimization problem such that it takes…

Optimization and Control · Mathematics 2024-06-21 Johannes Haubner , Michael Ulbrich

Mixed-dimensional elliptic equations exhibiting a hierarchical structure are commonly used to model problems with high aspect ratio inclusions, such as flow in fractured porous media. We derive general abstract estimates based on the theory…

Numerical Analysis · Mathematics 2022-04-21 Jhabriel Varela , Elyes Ahmed , Eirik Keilegavlen , Jan Martin Nordbotten , Florin Adrian Radu

We consider initial value problems where we are interested in a quantity of interest (QoI) that is the integral in time of a functional of the solution of the IVP. For these, we look into local error based time adaptivity. We derive a goal…

Numerical Analysis · Mathematics 2018-05-09 Peter Meisrimel , Philipp Birken

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 consider systems of ordinary differential equations with multiple scales in time. In general, we are interested in the long time horizon of a slow variable that is coupled to solution components that act on a fast scale. Although the…

Numerical Analysis · Mathematics 2021-04-28 Leopold Lautsch , Thomas Richter

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

The simulation of complex nonlinear engineering systems such as compressible fluid flows may be targeted to make more efficient and accurate the approximation of a specific (scalar) quantity of interest of the system. Putting aside modeling…

Numerical Analysis · Mathematics 2018-11-14 Jan Van Langenhove , Didier Lucor , Frédéric Alauzet , Anca Belme

We recently derived the unified continuum and variational multiscale formulation for fluid-structure interaction (FSI) using the Gibbs free energy. Restricting our attention to vascular FSI, we now reduce this arbitrary Lagrangian-Eulerian…

Computational Physics · Physics 2022-04-06 Ingrid S. Lan , Ju Liu , Weiguang Yang , Alison L. Marsden

This paper introduces a novel framework for model adaptivity in the context of heterogeneous multiscale problems. The framework is based on the idea to interpret model adaptivity as a minimization problem of local error indicators, that are…

Numerical Analysis · Mathematics 2017-12-04 Matthias Maier , Rolf Rannacher

We present an immersed boundary projection method formulated in a body-fixed frame of reference for flow-structure interaction (FSI) problems involving rigid bodies with complex geometries. The body-fixed formulation is aimed at maximizing…

Fluid Dynamics · Physics 2020-01-07 Tzu-Yuan Lin , Hsin-Yu Hsieh , Hsieh-Chen Tsai

We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising…

Numerical Analysis · Mathematics 2024-01-12 Roland Becker , Gregor Gantner , Michael Innerberger , Dirk Praetorius