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The Stokes-Brinkman equations model flow in heterogeneous porous media by combining the Stokes and Darcy models of flow into a single system of equations. With suitable parameters, the equations can model either flow without detailed…

Numerical Analysis · Mathematics 2019-08-28 Kevin Williamson , Pavel Burda , Bedřich Sousedík

The paper presents a workflow for fast pore-scale simulation of single-phase flow in tight reservoirs typically characterized by low, multiscale porosity. Multiscale porosity implies that the computational domain contains porous voxels…

Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…

Computational Engineering, Finance, and Science · Computer Science 2019-02-05 Bilen Emek Abali

We study a stationary model of doubly diffusive flows with temperature-dependent viscosity on bounded Lipschitz domains in two and three dimensions. A new well-posedness and regularity analysis of weak solutions under minimal assumptions on…

Numerical Analysis · Mathematics 2026-03-27 Jai Tushar , Arbaz Khan , Manil T. Mohan

We introduce a Darcy-scale model to describe compressible multi-component flow in a fully saturated porous medium. In order to capture cross-diffusive effects between the different species correctly, we make use of the Maxwell--Stefan…

Analysis of PDEs · Mathematics 2020-12-02 Lukas Ostrowski , Christian Rohde

This work is motivated by the need to develop efficient tools for uncertainty quantification in subsurface flows associated with radioactive waste disposal studies. We consider single phase flow problems in random porous media described by…

Numerical Analysis · Mathematics 2013-12-23 Ivan G. Graham , Robert Scheichl , Elisabeth Ullmann

This paper analyses the classical mixed finite element method (FEM) and a pressure-robust variant with divergence-free reconstruction operators for the coupled Stokes-Darcy problem. Its main contribution is to provide viscosity-explicit a…

Numerical Analysis · Mathematics 2026-02-02 Jiachuan Zhang

The correct choice of interface conditions and effective parameters for coupled macroscale free-flow and porous-medium models is crucial for a complete mathematical description of the problem under consideration and for accurate numerical…

Numerical Analysis · Mathematics 2019-06-27 Iryna Rybak , Christoph Schwarzmeier , Elissa Eggenweiler , Ulrich Rüde

A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…

Numerical Analysis · Mathematics 2022-01-03 Chuwen Ma , Weiying Zheng

We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…

Optimization and Control · Mathematics 2025-09-03 Mootta Prangprakhon , Nimit Nimana

We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isochoric flows of colloidal suspensions. The symmetric velocity…

Numerical Analysis · Mathematics 2021-08-09 Andrea Bonito , Vivette Girault , Diane Guignard , Kumbakonam R. Rajagopal , Endre Süli

In this paper we analyze the finite element approximation of the Stokes equations with non-smooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard…

Numerical Analysis · Mathematics 2019-12-12 Ricardo G. Durán , Lucia Gastaldi , Ariel L. Lombardi

A two-step preconditioned iterative method based on the Hermitian/Skew-Hermitian splitting is applied to the solution of nonsymmetric linear systems arising from the Finite Element approximation of convection-diffusion equations. The…

Numerical Analysis · Mathematics 2008-07-23 Alessandro Russo , Cristina Tablino Possio

We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity. For this problem, the classical finite elements method of degree one converges only to order one-half for the L2 norm of the vorticity. We…

Numerical Analysis · Mathematics 2024-12-16 François Dubois , Michel Salaün , Stéphanie Salmon

We present a hybrid-mixed finite element method for a novel hybrid-dimensional model of single-phase Darcy flow in a fractured porous media. In this model, the fracture is treated as an $(d-1)$-dimensional interface within the…

Numerical Analysis · Mathematics 2022-03-02 Guosheng Fu , Yang Yang

In this paper, an error analysis of a three steps two level Galekin finite element method for the two dimensional transient Navier-Stokes equations is discussed. First of all, the problem is discretized in spatial direction by employing…

Numerical Analysis · Mathematics 2014-01-23 Saumya Bajpai , Amiya K. Pani

We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle…

Computational Engineering, Finance, and Science · Computer Science 2020-06-24 Wen Yan , Eduardo Corona , Dhairya Malhotra , Shravan Veerapaneni , Michael Shelley

We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with…

Numerical Analysis · Mathematics 2015-12-11 Leonardo A. Poveda , Sebastian Huepo , Victor M. Calo , Juan Galvis

This paper is concerned with mixed finite element method (FEM) for solving the two-dimensional, nonlinear fourth-order active fluid equations. By introducing an auxiliary variable $w=-\Delta u$, the original fourth problem is transformed…

Numerical Analysis · Mathematics 2025-07-30 Nan Zheng , Xu Guo , Wenlong Pei , Wenju Zhao

We study a finite element computational model for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium. The free fluid is governed by the Stokes equations, while the flow in the…

Numerical Analysis · Mathematics 2017-10-19 Ilona Ambartsumyan , Eldar Khattatov , Ivan Yotov , Paolo Zunino