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In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…

Numerical Analysis · Mathematics 2023-01-13 Sebastian Schwarzacher , Bangwei She , Karel Tuma

We consider the approximation of the 2D frictionless contact problem in elasticity using the Virtual Element Methods (VEMs). To overcome the volumetric locking phenomenon in the nearly incompressible case, we adopt a mixed…

Numerical Analysis · Mathematics 2026-01-07 C. Lovadina , L. Molinari

This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the…

Numerical Analysis · Mathematics 2024-10-30 Xiaojuan Wang , Jihong Xiao , Xiaoping Xie , Shiquan Zhang

We describe and summarize a class of minimal numerical models emerged from recent development of simulation methods for dense particle suspensions in overdamped linear flows. The main ingredients include (i) a frame-invariant, short-range…

Soft Condensed Matter · Physics 2020-05-27 Zhouyang Ge , Luca Brandt

We extend the conforming virtual element method to the numerical resolution of eigenvalue problems with potential terms on a polytopal mesh. An important application is that of the Schrodinger equation with a pseudopotential term. This…

Numerical Analysis · Mathematics 2018-04-04 Ondrej Certik , Francesca Gardini , Gianmarco Manzini , Giuseppe Vacca

In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of…

Numerical Analysis · Computer Science 2019-10-23 Yongxing Wang , Peter K. Jimack , Mark A. Walkley

In this paper, we derive a variational integrator for certain highly oscillatory problems in mechanics. To do this, we take a new approach to the splitting of fast and slow potential forces: rather than splitting these forces at the level…

Numerical Analysis · Mathematics 2009-08-03 Ari Stern , Eitan Grinspun

In this article, we addressed the numerical solution of a non-linear evolutionary variational inequality, which is encountered in the investigation of quasi-static contact problems. Our study encompasses both the semi-discrete and…

Numerical Analysis · Mathematics 2024-01-05 Kamana Porwal , Tanvi Wadhawan

Simulation of fracturing processes in porous rocks can be divided into two main branches: (i) modeling the rock as a continuum which is enhanced with special features to account for fractures, or (ii) modeling the rock by a discrete (or…

Numerical Analysis · Mathematics 2017-02-07 Halvor Møll Nilsen , Idar Larsen , Xavier Raynaud

In this paper, we consider a nonlinear PDE system governed by a parabolic heat equation coupled in a nonlinear way with a hyperbolic momentum equation describing the behavior of a displacement field coupled with a nonlinear elliptic…

Numerical Analysis · Mathematics 2023-11-16 Maryam Parvizi , Amirreza Khodadadian , Thomas Wick

In this paper we develop a fully nonconforming virtual element method (VEM) of arbitrary approximation order for the two dimensional Cahn-Hilliard equation. We carry out the error analysis for the semidiscrete (continuous-in-time) scheme…

Numerical Analysis · Mathematics 2024-11-01 Andreas Dedner , Alice Hodson

A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then…

Computational Physics · Physics 2009-11-13 Anthony JC Ladd , Gaurav Misra

We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time…

Numerical Analysis · Mathematics 2022-09-26 Franco Dassi , Alessio Fumagalli , Ilario Mazzieri , Giuseppe Vacca

In this paper, we present a novel nodal integration scheme for meshfree Galerkin methods that draws on the mathematical framework of the virtual element method. We adopt linear maximum-entropy basis functions for the discretization of field…

Numerical Analysis · Mathematics 2020-01-01 R. Silva-Valenzuela , A. Ortiz-Bernardin , N. Sukumar , E. Artioli , N. Hitschfeld-Kahler

Numerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood.…

Numerical Analysis · Mathematics 2025-08-07 Nils Lange , Geralf Hütter , Bjoern Kiefer

The XDEM multi-physics and multi-scale simulation platform roots in the Ex- tended Discrete Element Method (XDEM) and is being developed at the In- stitute of Computational Engineering at the University of Luxembourg. The platform is an…

Computational Engineering, Finance, and Science · Computer Science 2018-08-27 Bernhard Peters , Maryam Baniasadi , Mehdi Baniasadi , Xavier Besseron , Alvaro Estupinan Donoso , Mohammad Mohseni , Gabriele Pozzetti

An energetically balanced, implicit integrator for non-hydrostatic vertical atmospheric dynamics on the sphere is presented. The integrator allows for the exact balance of energy exchanges in space and time for vertical atmospheric motions…

Numerical Analysis · Mathematics 2020-12-01 David Lee

Hamiltonian splitting methods are an established technique to derive stable and accurate integration schemes in molecular dynamics, in which additional accuracy can be gained using force gradients. For rigid bodies, a tradition exists in…

Statistical Mechanics · Physics 2008-04-10 Ramses van Zon , Igor P. Omelyan , Jeremy Schofield

In this work, we investigate Vacuum-Packed Particle (VPP) dampers -- granular-core dampers offering tunable damping performance -- as a more sustainable alternative to conventional systems such as magnetorheological fluid dampers. A…

Materials Science · Physics 2025-09-08 Pawel Chodkiewicz , Robert Zalewski , Jakub Lengiewicz

This article presents a priori error estimates of the miscible displacement of one compressible fluid by another in a porous medium. The study utilizes the $H(\rm div)$ conforming virtual element method (VEM) for the approximation of the…

Numerical Analysis · Mathematics 2024-05-13 Sarvesh Kumar , Devika Shylaja