English
Related papers

Related papers: Optimisation-Based Coupling of Finite Element Mode…

200 papers

This paper presents a rigorous finite element framework for solving an optimal control problem governed by the steady Navier-Stokes-Brinkman equations, focusing on identifying a scalar permeability parameter $\gamma$ from local velocity…

Numerical Analysis · Mathematics 2025-03-12 Jorge Aguayo Araneda , Julie Merten

We investigate the use of reduced-order modelling to run discrete element simulations at higher speeds. Taking a data-driven approach, we run many offline simulations in advance and train a model to predict the velocity field from the mass…

Computational Physics · Physics 2021-03-02 Erik Wallin , Martin Servin

Reduced order models play an important role in the design, optimization and control of dynamical systems. In recent years, there has been an increasing interest in the application of data-driven techniques for model reduction that can…

Fluid Dynamics · Physics 2021-02-23 Carlos J. G. Rojas , Andreas Dengel , Mateus Dias Ribeiro

We consider two-level finite element discretization methods for the stream function formulation of the Navier-Stokes equations. The two-level method consists of solving a small nonlinear system on the coarse mesh, then solving a linear…

Numerical Analysis · Mathematics 2025-10-20 Faisal Fairag

Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…

Dynamical Systems · Mathematics 2026-03-19 Akira Saito , Masato Tanaka

An efficient and accurate finite-element algorithm is described for the numerical solution of the incompressible Navier-Stokes (INS) equations. The new algorithm that solves the INS equations in a velocity-pressure reformulation is based on…

Numerical Analysis · Mathematics 2020-02-19 Longfei Li

We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…

We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy…

Numerical Analysis · Mathematics 2021-05-14 Juan Pablo Borthagaray , Wenbo Li , Ricardo H. Nochetto

Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and…

Computational Engineering, Finance, and Science · Computer Science 2024-01-22 Seung Whan Chung , Youngsoo Choi , Pratanu Roy , Thomas Moore , Thomas Roy , Tiras Y. Lin , Du Y. Nguyen , Christopher Hahn , Eric B. Duoss , Sarah E. Baker

Predictive modeling involving simulation and sensor data at the same time, is a growing challenge in computational science. Even with large-scale finite element models, a mismatch to the sensor data often remains, which can be attributed to…

Computational Engineering, Finance, and Science · Computer Science 2025-12-01 Lucas Hermann , Matthias Bollhöfer , Ulrich Römer

Standard ROMs generally yield spurious numerical oscillations in the simulation of convection-dominated flows. Regularized ROMs use explicit ROM spatial filtering to decrease these spurious numerical oscillations. The Leray ROM is a…

Numerical Analysis · Mathematics 2017-02-20 Xuping Xie , David Wells , Zhu Wang , Traian Iliescu

In this article we propose two finite element schemes for the Navier-Stokes equations, based on a reformulation that involves differential operators from the de Rham sequence and an advection operator with explicit skew-symmetry in weak…

Numerical Analysis · Mathematics 2023-06-27 Valentin Carlier , Martin Campos Pinto , Francesco Fambri

The flux-mortar mixed finite element method was recently developed for a general class of domain decomposition saddle point problems on non-matching grids. In this work we develop the method for Darcy flow using the multipoint flux…

Numerical Analysis · Mathematics 2023-01-18 Wietse M. Boon , Dennis Gläser , Rainer Helmig , Ivan Yotov

Partial differential equation-based numerical solution frameworks for initial and boundary value problems have attained a high degree of complexity. Applied to a wide range of physics with the ultimate goal of enabling engineering…

Numerical Analysis · Mathematics 2021-05-11 Matthew Duschenes , Krishna Garikipati

Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…

Optimization and Control · Mathematics 2015-11-06 Anna Fiedler , Fabian J. Theis , Jan Hasenauer

We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier-Stokes equations. Our algorithm is based on an approximated…

Numerical Analysis · Mathematics 2021-04-07 Luca Pegolotti , Martin Pfaller , Alison Marsden , Simone Deparis

In this work, a new discretization approach for coupled free and porous-medium flows is introduced, which uses a finite volume staggered-grid method for the discretization of the Navier-Stokes equations in the free-flow subdomain, while a…

Numerical Analysis · Mathematics 2021-12-22 Martin Schneider , Dennis Gläser , Kilian Weishaupt , Edward Coltman , Bernd Flemisch , Rainer Helmig

This work investigates projection-based Reduced-Order Models (ROMs) formulated in the frequency domain, employing a space-time basis constructed with Spectral Proper Orthogonal Decomposition to efficiently represent dominant spatio-temporal…

Fluid Dynamics · Physics 2026-01-12 Xiaodong Li , Davide Lasagna

We consider the numerical approximation of a sharp-interface model for two-phase flow, which is given by the incompressible Navier-Stokes equations in the bulk domain together with the classical interface conditions on the interface. We…

Numerical Analysis · Mathematics 2023-06-21 Harald Garcke , Robert Nürnberg , Quan Zhao

Traditional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) suffer from severe limitations when dealing with nonlinear time-dependent parametrized PDEs,…

Numerical Analysis · Mathematics 2020-01-14 Stefania Fresca , Luca Dede , Andrea Manzoni