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We develop and analyse an adaptive fully mixed finite element method for stationary generalized bioconvective flows, where the Navier--Stokes equations with concentration-dependent viscosity are coupled with a conservation law for swimming…

Numerical Analysis · Mathematics 2026-01-14 Eligio Colmenares , Ricardo Ruiz-Baier , Dalidet Sanhueza

In this work, we extend the equal-order stabilized scheme discussed in [Franca et al., Comput. Methods Appl. Mech. Engrg. 99 (1992) 209-233] to accommodate slip (i.e., Navier) boundary conditions for the stationary Navier-Stokes equations.…

Numerical Analysis · Mathematics 2025-01-27 Aparna Bansal , Nicolás Barnafi , Rodolfo Araya , Dwijendra Narain Pandey

We develop a mixed finite element method for the coupled problem arising in the interaction between a free fluid governed by the Stokes equations and flow in deformable porous medium modeled by the Biot system of poroelasticity. Mass…

Numerical Analysis · Mathematics 2021-12-16 Tongtong Li , Ivan Yotov

We summarise three applications of the obstacle problem to membrane contact, elastoplastic torsion and cavitation modelling, and show how the resulting models can be solved using mixed finite elements. It is challenging to construct fixed…

Numerical Analysis · Mathematics 2026-01-28 Tom Gustafsson

We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…

Numerical Analysis · Mathematics 2018-10-18 Ruchi Guo , Tao Lin , Yanping Lin

Interfacial energy plays an important role in equilibrium morphologies of nanosized microstructures of solid materials due to the high interface-to-volume ratio, and can no longer be neglected as it does in conventional mechanics analysis.…

Numerical Analysis · Mathematics 2012-10-22 Xujun Zhao , Stéphane P. A. Bordas , Jianmin Qu

In this paper we develop a simple finite element method for simulation of embedded layers of high permeability in a matrix of lower permeability using a basic model of Darcy flow in embedded cracks. The cracks are allowed to cut through the…

Numerical Analysis · Mathematics 2017-09-05 Erik Burman , Peter Hansbo , Mats G. Larson

In this paper, we study an interaction problem between a $3D$ compressible viscous fluid and a $3D$ nonlinear viscoelastic solid fully immersed in the fluid, coupled together on the interface surface. The solid is allowed to have…

Analysis of PDEs · Mathematics 2023-12-20 Malte Kampschulte , Boris Muha , Srđan Trifunović

We introduce a new multimesh finite element method for direct numerical simulation of incompressible particulate flows. The proposed approach falls into the category of overlapping domain decomposition / Chimera / overset grid meshes. In…

Numerical Analysis · Mathematics 2025-07-01 Raphael Münster , Otto Mierka , Dmitri Kuzmin , Stefan Turek

In this note we design a cut finite element method for a low order divergence free element applied to a boundary value problem subject to Stokes' equations. For the imposition of Dirichlet boundary conditions we consider either Nitsche's…

Numerical Analysis · Mathematics 2023-11-14 Erik Burman , Peter Hansbo , Mats G. Larson

In this paper, we investigate a chemotaxis-fluid interaction model governed by the incompressible Navier-Stokes equations coupled with the classical Keller-Segel chemotaxis system. To numerically solve this coupled system, we develop a…

Numerical Analysis · Mathematics 2025-12-01 Chenyang Li , Ping Lin , Haibiao Zheng

We define a new finite element method for a steady state elliptic problem with discontinuous diffusion coefficients where the meshes are not aligned with the interface. We prove optimal error estimates in the $L^2$ norm and $H^1$ weighted…

Numerical Analysis · Mathematics 2016-10-18 Johnny Guzman , Manuel A. Sanchez , Marcus Sarkis

The present article proposes a partitioned Dirichlet-Neumann algorithm, that allows to address unique challenges arising from a novel mixed-dimensional coupling of very slender fibers embedded in fluid flow using a regularized mortar-type…

Numerical Analysis · Mathematics 2023-12-04 Nora Hagmeyer , Matthias Mayr , Alexander Popp

In this paper, we introduce a novel unfitted finite element method to solve the quad-curl interface problem. We adapt Nitsche's method for curlcurl-conforming elements and double the degrees of freedom on interface elements. To ensure…

Numerical Analysis · Mathematics 2023-11-28 Hailong Guo , Mingyan Zhang , Qian Zhang , Zhimin Zhang

We develop finite element methods for coupling the steady-state Onsager--Stefan--Maxwell equations to compressible Stokes flow. These equations describe multicomponent flow at low Reynolds number, where a mixture of different chemical…

Numerical Analysis · Mathematics 2022-09-26 Francis R. A. Aznaran , Patrick E. Farrell , Charles W. Monroe , Alexander J. Van-Brunt

The isogeometric approximation of the Stokes problem in a trimmed domain is studied. This setting is characterized by an underlying mesh unfitted with the boundary of the physical domain making the imposition of the essential boundary…

Numerical Analysis · Mathematics 2022-02-02 Riccardo Puppi

In this work, we consider unfitted finite element methods for the numerical approximation of the Stokes problem. It is well-known that this kind of methods lead to arbitrarily ill-conditioned systems. In order to solve this issue, we…

Numerical Analysis · Mathematics 2021-09-30 Santiago Badia , Alberto F. Martín , Francesc Verdugo

We study the existence of weak martingale solutions to a stochastic moving boundary problem arising from the interaction between an isentropic compressible fluid and a viscoelastic structure. In the model, we consider a three-dimensional…

Analysis of PDEs · Mathematics 2025-05-22 Jeffrey Kuan , Krutika Tawri

In this work a Nitsche-based imposition of generalized Navier conditions on cut meshes for the Oseen problem is presented. Other methods from literature dealing with the generalized Navier condition impose this condition by means of…

Numerical Analysis · Mathematics 2018-02-14 M. Winter , B. Schott , A. Massing , W. A. Wall

In this article we present a goal-oriented adaptive finite element method for a class of subsurface flow problems in porous media, which exhibit seepage faces. We focus on a representative case of the steady state flows governed by a…

Numerical Analysis · Mathematics 2021-01-12 Ben Ashby , Cassiano Bortolozo , Alex Lukyanov , Tristan Pryer