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This paper investigates a modification of the fictitious domain method with continuation in the lower-order coefficients for the unsteady Navier-Stokes equations governing the motion of an incompressible homogeneous fluid in a bounded 2D or…

Numerical Analysis · Mathematics 2025-12-23 Zhanybek Baitulenov , Maxim Olshanskii , Almas Temirbekov , Nurlan Temirbekov , Syrym Kasenov

We introduce a new abstraction for the representation and solution of multi-domain problems using finite element methods. This is an advance over previous work in that it achieves a single higher-level abstraction that represents…

Mathematical Software · Computer Science 2025-12-09 Koki Sagiyama , Lawrence Mitchell , David A. Ham

In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…

Numerical Analysis · Mathematics 2014-12-09 Sven Gross , Maxim A. Olshanskii , Arnold Reusken

Loosely coupled partitioned methods for multiphysics problems treat each subproblem as a separate entity and advance them independently in time. In so doing these methods enable code reuse, increase concurrency and provide a convenient…

Computational Engineering, Finance, and Science · Computer Science 2025-07-31 Pavel Bochev , Justin Owen , Paul Kuberry , Jeffrey Connors

This work is concerned with the propagation of uncertainty across coupled domain problems with high-dimensional random inputs. A stochastic model reduction approach based on low-rank separated representations is proposed for the partitioned…

Probability · Mathematics 2015-06-16 Mohammad Hadigol , Alireza Doostan , Hermann G. Matthies , Rainer Niekamp

This paper presents a pressure-robust discretizations, specifically within the context of optimal control problems for the Stokes-Darcy system. The study meticulously revisits the formulation of the divergence constraint and the enforcement…

Numerical Analysis · Mathematics 2025-02-25 Jingshi Li , Jiachuan Zhang , Ran Zhang

The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the…

Computational Physics · Physics 2012-02-20 J. E. Sprittles , Y. D. Shikhmurzaev

A framework is developed for a robust and highly accurate numerical solution of the coupled Stokes-Darcy system in three dimensions. The domain decomposition method is based on a Dirichlet-Neumann type splitting of the interface conditions…

Numerical Analysis · Mathematics 2022-01-19 Svetlana Tlupova

We develop a cut finite element method for the Darcy problem on surfaces. The cut finite element method is based on embedding the surface in a three dimensional finite element mesh and using finite element spaces defined on the three…

Numerical Analysis · Mathematics 2017-10-11 Peter Hansbo , Mats G. Larson , Andre Massing

In this paper we introduce a mixed virtual element method to approximate the solution for the two dimensional generalized Oseen problem. We introduce the pseudostress as an additional unknown, which allows to eliminate the pressure from the…

Numerical Analysis · Mathematics 2026-01-29 Felipe Lepe , Gonzalo Rivera

Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…

Fluid Dynamics · Physics 2025-12-24 Thomas Leyssens , Jonathan Lambrechts , Jean-François Remacle

We develop a space-time mortar mixed finite element method for parabolic problems. The domain is decomposed into a union of subdomains discretized with non-matching spatial grids and asynchronous time steps. The method is based on a…

Numerical Analysis · Mathematics 2021-10-06 Manu Jayadharan , Michel Kern , Martin Vohralík , Ivan Yotov

We present a novel stabilized isogeometric formulation for the Stokes problem, where the geometry of interest is obtained via overlapping NURBS (non-uniform rational B-spline) patches, i.e., one patch on top of another in an arbitrary but…

Numerical Analysis · Mathematics 2023-09-22 Xiaodong Wei , Riccardo Puppi , Pablo Antolin , Annalisa Buffa

In this paper a class of higher order finite element methods for the discretization of surface Stokes equations is studied. These methods are based on an unfitted finite element approach in which standard Taylor-Hood spaces on an underlying…

Numerical Analysis · Mathematics 2019-09-19 Thomas Jankuhn , Arnold Reusken

Stokes flows are a type of fluid flow where convective forces are small in comparison with viscous forces, and momentum transport is entirely due to viscous diffusion. Besides being routinely used as benchmark test cases in numerical fluid…

Numerical Analysis · Mathematics 2021-12-16 Andrea Cioncolini , Daniele Boffi

In this article, we introduce a new partially penalized immersed finite element method (IFEM) for solving elliptic interface problems with multi-domains and triple-junction points. We construct new IFE functions on elements intersected with…

Numerical Analysis · Mathematics 2020-03-04 Yuan Chen , Songming Hou , Xu Zhang

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

In this work, we generalize the mass-conserving mixed stress (MCS) finite element method for Stokes equations [Gopalakrishnan J., Lederer P., and Sch\"oberl J., A mass conserving mixed stress formulation for the Stokes equations, IMA…

Numerical Analysis · Mathematics 2025-09-19 Guosheng Fu , Michael Neunteufel , Joachim Schöberl , Adam Zdunek

In this work, we couple a high-accuracy phase-field fracture reconstruction approach iteratively to fluid-structure interaction. The key motivation is to utilize phase-field modelling to compute the fracture path. A mesh reconstruction…

Numerical Analysis · Mathematics 2024-08-19 Henry von Wahl , Thomas Wick

In this paper, we introduce a new finite element method for solving the Stokes equations in the primary velocity-pressure formulation. This method employs $H(div)$ finite elements to approximate velocity, which leads to two unique…

Numerical Analysis · Mathematics 2020-06-23 Xiu Ye , Shangyou Zhang