There has been an arising trend of adopting deep learning methods to study partial
differential equations (PDEs). This article is to propose a kind of coupled physics-informed …

In this paper, we propose and investigate an efficient method called CDNNs (Coupled Deep
Neural Networks) for the time-dependent coupled Stokes-Darcy problems. Specifically, we …

In this paper, some local and parallel finite element methods based on two-grid
discretizations are proposed and investigated for a non-stationary coupled Stokes-Darcy …

This paper develops novel finite element solvers for linear poroelasticity problems on
quadrilateral meshes. These solvers are based on the primal formulations of linear elasticity …

In this paper we propose a locally conservative, lowest-order staggered discontinuous
Galerkin method for the coupled Stokes–Darcy problem on general quadrilateral and …

In this article, we develop the physics informed neural networks (PINNs) coupled with small
sample learning for solving the transient Stokes equations. Specifically, the governing …

In this paper, we propose a new numerical scheme for the coupled Stokes-Darcy model with
the Beavers-Joseph-Saffman interface condition. We use the weak Galerkin method to …

In this paper, we present a second-order decoupled scheme based on the artificial
compression method for the time-dependent Stokes-Darcy equations. This method not only …

We present an efficient deep learning method called coupled deep neural networks
(CDNNs) for coupling of the Stokes and Darcy–Forchheimer problems. Our method …

In this paper, a weighted discontinuous Galerkin finite element method and an upwind
format are presented to solve the coupled Brinkman–Darcy flow and transport model. The …