The main purpose of this monograph is to provide a simple and accessible introduction to
the mixed finite element method as a fundamental tool to numerically solve a wide class of …

In this paper, we consider the numerical approximation for a phase field model of the
coupled two-phase free flow and two-phase porous media flow. This model consists of Cahn …

In this article a domain decomposition method is proposed to solve a time-dependent Navier-
Stokes-Darcy model with Beavers-Joseph interface condition and defective boundary …

In this article we consider the numerical modeling and simulation via the phase field
approach for coupled two-phase free flow and two-phase porous media flow of different …

A family of weak Galerkin finite element discretizations is developed for solving the coupled
Darcy–Stokes equation. The equation in consideration admits the Beaver–Joseph–Saffman …

Variational Techniques for Elliptic Partial Differential Equations, intended for graduate
students studying applied math, analysis, and/or numerical analysis, provides the necessary …

In this paper, we propose and analyze two stabilized mixed finite element methods for the
dual‐porosity‐Stokes model, which couples the free flow region and microfracture‐matrix …

This paper presents a weak virtual element method on general meshes for the Stokes–
Darcy problem with the Beavers–Joseph–Saffman interface condition. The velocity is …

In this paper, we present a stabilized finite volume element method with the conforming finite
element triples P 1–P 0–P 1 and P 1–P 1–P 1 for approximating the velocity, pressure, and …

In this paper we introduce and analyze two new fully-mixed variational formulations for the
coupling of fluid flow with porous media flow. Flows are governed by the Stokes and Darcy …