Staggered DG Method for Coupling of the Stokes and Darcy--Forchheimer Problems

DOI10.1137/19M1268525zbMath1456.65172arXiv1906.06652OpenAlexW3118878610MaRDI QIDQ5147754

Guanyu Zhou, Eric T. Chung, Li-Na Zhao, Eun-Jae Park

Publication date: 28 January 2021

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.06652

zbMATH Keywords

Stokes equationsnonmatching gridsDarcy-Forchheimer equationsBeavers-Joseph-Saffman interface conditionsstaggered DG methodhighly distorted grids

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (10)

A uniformly robust staggered DG method for the unsteady Darcy-Forchheimer-Brinkman problem ⋮ A Robin-Type Domain Decomposition Method for a Novel Mixed-Type DG Method for the Coupled Stokes--Darcy Problem ⋮ Nonstandard finite element methods. Abstracts from the workshop held January 10--16, 2021 (hybrid meeting) ⋮ A staggered cell-centered DG method for the biharmonic Steklov problem on polygonal meshes: a priori and a posteriori analysis ⋮ A staggered discontinuous Galerkin method for quasi-linear second order elliptic problems of nonmonotone type ⋮ An adaptive discontinuous Galerkin method for the Darcy system in fractured porous media ⋮ Unnamed Item ⋮ Multiscale mortar mixed domain decomposition approximations of nonlinear parabolic equations ⋮ Staggered DG method with small edges for Darcy flows in fractured porous media ⋮ Efficient coupled deep neural networks for the time-dependent coupled Stokes-Darcy problems

Cites Work

• Unnamed Item
• Unnamed Item
• An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators
• Analysis of a discontinuous finite element method for the coupled Stokes and Darcy problems
• Numerical discretization of a Darcy-Forchheimer model
• A multiscale finite element method for elliptic problems in composite materials and porous media
• A priori and a posteriori error analysis of a staggered discontinuous Galerkin method for convection dominant diffusion equations
• Guaranteed a posteriori error estimates for a staggered discontinuous Galerkin method
• A posteriori error estimates for the virtual element method
• Mathematical and numerical models for coupling surface and groundwater flows
• Fully discrete mixed finite element approximations for non-Darcy flows in porous media
• A staggered DG method of minimal dimension for the Stokes equations on general meshes
• Fully computable bounds for a staggered discontinuous Galerkin method for the Stokes equations
• Mortar formulation for a class of staggered discontinuous Galerkin methods
• Convergence and superconvergence of staggered discontinuous Galerkin methods for the three-dimensional Maxwell's equations on Cartesian grids
• A unified stabilized method for Stokes' and Darcy's equations
• Discontinuous Galerkin and mimetic finite difference methods for coupled Stokes-Darcy flows on polygonal and polyhedral grids
• Mortar multiscale finite element methods for Stokes-Darcy flows
• A Two-Grid Block-Centered Finite Difference Method For Darcy--Forchheimer Flow in Porous Media
• Optimal Discontinuous Galerkin Methods for the Acoustic Wave Equation in Higher Dimensions
• Analysis of fully-mixed finite element methods for the Stokes-Darcy coupled problem
• A weak Galerkin mixed finite element method for second order elliptic problems
• On the Boundary Condition at the Surface of a Porous Medium
• Coupling Fluid Flow with Porous Media Flow
• Poincaré--Friedrichs Inequalities for Piecewise H¹ Functions
• An Unfitted Hybrid High-Order Method for Elliptic Interface Problems
• A Staggered Discontinuous Galerkin Method of Minimal Dimension on Quadrilateral and Polygonal Meshes
• Locally Conservative Coupling of Stokes and Darcy Flows
• Mixed finite element methods for generalized Forchheimer flow in porous media
• Mixed Finite Element Methods for Nonlinear Second-Order Elliptic Problems
• A Block-Centered Finite Difference Method for the Darcy--Forchheimer Model
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• A fully mixed finite element method for the coupling of the Stokes and Darcy–Forchheimer problems
• A stabilized Crouzeix‐Raviart element method for coupling stokes and darcy‐forchheimer flows
• A Staggered Discontinuous Galerkin Method for the Stokes System
• Optimal Discontinuous Galerkin Methods for Wave Propagation
• The Mathematical Theory of Finite Element Methods
• Finite Elements

This page was built for publication: Staggered DG Method for Coupling of the Stokes and Darcy--Forchheimer Problems