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We consider a poromechanics model including frictionless contact mechanics. The resulting model consists of the Biot equations with contact boundary conditions leading to a variational inequality modelling mechanical deformations coupled to…

Numerical Analysis · Mathematics 2024-07-19 Tameem Almani , Kundan Kumar

We develop a unified continuum modeling framework for viscous fluids and hyperelastic solids using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the…

Computational Physics · Physics 2020-03-03 Ju Liu , Alison L. Marsden

We investigate several robust preconditioners for solving the saddle-point linear systems that arise from spatial discretization of unsteady and steady variable-coefficient Stokes equations on a uniform staggered grid. Building on the…

Numerical Analysis · Mathematics 2016-08-24 M. Cai , A. J. Nonaka , J. B. Bell , B. E. Griffith , A. Donev

We develop a computational model to study the interaction of a fluid with a poroelastic material. The coupling of Stokes and Biot equations represents a prototype problem for these phenomena, which feature multiple facets. On one hand it…

Numerical Analysis · Mathematics 2023-07-19 Martina Bukac , Ivan Yotov , Rana Zakerzadeh , Paolo Zunino

A mechanical model and finite element method for the simultaneous solution of Stokes and incompressible Navier-Stokes flows on multiple curved surfaces over a bulk domain are proposed. The two-dimensional surfaces are defined implicitly by…

Computational Engineering, Finance, and Science · Computer Science 2025-10-09 Michael Wolfgang Kaiser , Thomas-Peter Fries

A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a BGK collision operator using the lattice Boltzmann method to simulate binary fluid…

Soft Condensed Matter · Physics 2018-05-09 Nicolas Rivas , Stefan Frijters , Ignacio Pagonabarraga , Jens Harting

The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in three-dimensional space. The method employs generalized Taylor-Hood finite element pairs on tetrahedral bulk mesh to discretize the…

Numerical Analysis · Mathematics 2020-03-17 Thomas Jankuhn , Maxim A. Olshanskii , Arnold Reusken , Alexander Zhiliakov

We present a stabilized, structure-preserving finite element framework for solving the Vlasov-Maxwell equations. The method uses a tensor product of continuous polynomial spaces for the spatial and velocity domains, respectively, to…

Numerical Analysis · Mathematics 2025-11-17 Katharina Kormann , Murtazo Nazarov , Junjie Wen

Discrete particle simulations are widely used to study large-scale particulate flows in complex geometries where particle-particle and particle-fluid interactions require an adequate representation but the computational cost has to be kept…

Computational Engineering, Finance, and Science · Computer Science 2017-11-02 Christoph Rettinger , Ulrich Rüde

We consider a 1D-2V Vlasov-Fokker-Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we…

Plasma Physics · Physics 2018-05-09 William T. Taitano , Luis Chacon , Andrei N. Simakov

We consider a bulk-membrane-coupled partial differential equation in which a single diffusion equation posed within the unit ball is coupled to a two-component reaction diffusion equation posed on the bounding unit sphere through a linear…

Pattern Formation and Solitons · Physics 2019-10-21 Daniel Gomez

This paper presents a new monolithic free-surface formulation that exhibits correct kinetic and potential energy behavior. We focus in particular on the temporal energy behavior of two-fluids flow with varying densities. Correct energy…

Numerical Analysis · Mathematics 2019-01-11 I. Akkerman , M. ten Eikelder

A new approach is introduced for deriving a mixed variational formulation for Kirchhoff plate bending problems with mixed boundary conditions involving clamped, simply supported, and free boundary parts. Based on a regular decomposition of…

Numerical Analysis · Mathematics 2017-12-21 Katharina Rafetseder , Walter Zulehner

In this paper, we consider the Stokes problem with Dirichlet boundary conditions and the constant kinematic viscosity $\nu$ in an axis-aligned domain $\Omega$. We decouple the velocity $\bm u$ and pressure $p$ by deriving a novel biharmonic…

Numerical Analysis · Mathematics 2025-06-17 Qiwei Feng , Bin Han , Michael Neilan

In this paper, we investigate the combination of a linear continuous interior penalty type and a non-linear artificial diffusion stabilisation applied to the transport problem, based on continuous Galerkin finite elements in space. This…

Numerical Analysis · Mathematics 2026-04-24 Erik Burman , Fabian Heimann

In this paper we consider a three-field formulation of the Biot model which has the displacement, the total pressure, and the pore pressure as unknowns. For parameter-robust stability analysis, we first show a priori estimates of the…

Numerical Analysis · Mathematics 2018-07-02 Jeonghun J. Lee

In this paper, we describe a stable finite element formulation for advection-diffusion-reaction problems that allows for robust automatic adaptive strategies to be easily implemented. We consider locally vanishing, heterogeneous, and…

Numerical Analysis · Mathematics 2021-09-01 Roberto J. Cier , Sergio Rojas , Victor M. Calo

We develop a Nitsche-based formulation for a general class of stabilized finite element methods for the Stokes problem posed on a pair of overlapping, non-matching meshes. By ex- tending the least-squares stabilization to the overlap…

Numerical Analysis · Mathematics 2012-05-30 André Massing , Mats G. Larson , Anders Logg , Marie E. Rognes

A simple, yet efficient procedure to solve quasistatic problems of special linear visco-elastic solids at small strains with equal rheological response in all tensorial components, utilizing boundary element method (BEM), is introduced.…

Numerical Analysis · Mathematics 2014-02-27 C. G. Panagiotopoulos , V. Mantic , T. Roubicek

In this work, we design and analyze semi/fully-discrete virtual element approximations for the time-dependent Navier--Stokes-Cahn--Hilliard equations, modeling the dynamics of two-phase incompressible fluid flows with diffuse interfaces. A…

Numerical Analysis · Mathematics 2026-01-27 Alberth Silgado , Giuseppe Vacca