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In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn-Hilliard equations, Navier-Stokes equations and…

Numerical Analysis · Mathematics 2022-02-01 Xiaorong Wang , Xiaodi Zhang

We consider a time-dependent coupled Navier--Stokes/generalized poroelastic flow problem and propose a unified and monolithic finite element discretization based on implicit time stepping. To handle the fluid-structure interface we employ a…

Numerical Analysis · Mathematics 2026-05-19 Aparna Bansal , Nicolas A. Barnafi , Dwijendra Narain Pandey , Ricardo Ruiz-Baier

As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we…

Numerical Analysis · Mathematics 2018-10-22 Christoph Erath , Günther Of , Francisco-Javier Sayas

This paper considers a large class of linear operator equations, including linear boundary value problems for partial differential equations, and treats them as linear recovery problems for objects from their data. Well-posedness of the…

Numerical Analysis · Mathematics 2014-03-17 Robert Schaback

In this paper, we present a novel solution strategy for the Cahn-Hilliard-Biot model, a three-way coupled system that features the interplay of solid phase separation, fluid dynamics, and elastic deformations in porous media. It is a…

Numerical Analysis · Mathematics 2026-02-02 Cedric Riethmüller , Erlend Storvik

We introduce new control-volume finite-element discretization schemes suitable for solving the Stokes problem. Within a common framework, we present different approaches for constructing such schemes. The first and most established strategy…

Numerical Analysis · Mathematics 2025-02-05 Martin Schneider , Timo Koch

The aim of the present study is to derive the effective quasi-static behaviour of a composite medium, made of a poroelastic matrix containing elastic impervious inclusions. For this purpose, the asymptotic homogenisation method is used. On…

Soft Condensed Matter · Physics 2019-02-15 Pascale Royer , Pierre Recho , Claude Verdier

In this paper, we construct and analyze a block dual-primal preconditioner for Biot's consolidation model approximated by three-field mixed finite elements based on a displacement, pressure, and total pressure formulation. The domain is…

Numerical Analysis · Mathematics 2025-04-08 Hanyu Chu , Luca Franco Pavarino , Stefano Zampini

A finite element discretization is developed for the Cai-Hu model, describing the formation of biological networks. The model consists of a non linear elliptic equation for the pressure $p$ and a non linear reaction-diffusion equation for…

Numerical Analysis · Mathematics 2025-03-28 Clarissa Astuto , Daniele Boffi , Fabio Credali

A multiphysics data analytic platform is established for imaging poroelastic interfaces of finite permeability (e.g., hydraulic fractures) from elastic waveforms and/or acoustic pore pressure measurements. This is accomplished through…

Numerical Analysis · Mathematics 2022-03-02 Fatemeh Pourahmadian , Kevish Napal

We develop a family of mixed finite element methods for a model of nonlinear poroelasticity where, thanks to a rewriting of the constitutive equations, the permeability depends on the total poroelastic stress and on the fluid pressure and…

Numerical Analysis · Mathematics 2025-02-25 Arbaz Khan , Bishnu P. Lamichhane , Ricardo Ruiz-Baier , Segundo Villa-Fuentes

In this paper, we investigate optimal control problems governed by the parabolic interface equation, in which the control acts on the interface. The solution to this problem exhibits low global regularity due to the jump of the coefficient…

Numerical Analysis · Mathematics 2025-10-15 Xindan Zhang , Jianping Zhao , Yanren Hou

Variable viscosity arises in many flow scenarios, often imposing numerical challenges. Yet, discretisation methods designed specifically for non-constant viscosity are few, and their analysis is even scarcer. In finite element methods for…

Numerical Analysis · Mathematics 2024-11-05 Felipe Galarce , Douglas R. Q. Pacheco

We present a theorem that allows to simplify linear stability analysis of periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems (both conservative and dissipative) with different kinds of discrete symmetry. This…

Pattern Formation and Solitons · Physics 2009-11-11 G. M. Chechin , K. G. Zhukov

In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase…

Analysis of PDEs · Mathematics 2019-02-20 Pierluigi Colli , Gianni Gilardi , Pavel Krejčí , Paolo Podio-Guidugli , Jürgen Sprekels

In computational fluid dynamics, the demand for increasingly multidisciplinary reliable simulations, for both analysis and design optimization purposes, requires transformational advances in individual components of future solvers. At the…

We develop a mixed finite element domain decomposition method on non-matching grids for the Biot system of poroelasticity. A displacement-pressure vector mortar function is introduced on the interfaces and utilized as a Lagrange multiplier…

Numerical Analysis · Mathematics 2024-09-13 Manu Jayadharan , Ivan Yotov

In this paper, we study the stability of various difference approximations of the Euler-Korteweg equations. This system of evolution PDEs is a classical isentropic Euler system perturbed by a dispersive (third order) term. The Euler…

Numerical Analysis · Mathematics 2014-01-30 Pascal Noble , Jean-Paul Vila

Across many scientific domains, practitioners rely on coarse, discretized summaries to track the evolving structure of complex systems under noise, measurement error, and changing system size. Understanding when such summaries are reliable…

Algebraic Topology · Mathematics 2026-01-29 Chad M. Topaz

We show short-time well-posedness of a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…

Analysis of PDEs · Mathematics 2026-05-01 Helmut Abels , Jonas Haselböck