DeepAI AI Chat
Log In Sign Up

Robust monolithic solvers for the Stokes-Darcy problem with the Darcy equation in primal form

10/14/2021
by   Wietse M. Boon, et al.
0

We construct mesh-independent and parameter-robust monolithic solvers for the coupled primal Stokes-Darcy problem. Three different formulations and their discretizations in terms of conforming and non-conforming finite element methods and finite volume methods are considered. In each case, robust preconditioners are derived using a unified theoretical framework. In particular, the suggested preconditioners utilize operators in fractional Sobolev spaces. Numerical experiments demonstrate the parameter-robustness of the proposed solvers.

READ FULL TEXT

page 1

page 2

page 3

page 4

01/15/2020

Robust preconditioning for coupled Stokes-Darcy problems with the Darcy problem in primal form

The coupled Darcy-Stokes problem is widely used for modeling fluid trans...
03/31/2023

Parameter-free preconditioning for nearly-incompressible linear elasticity

It is well known that via the augmented Lagrangian method, one can solve...
11/28/2022

Domain decomposition solvers for operators with fractional interface perturbations

Operators with fractional perturbations are crucial components for robus...
12/19/2022

The pressure-wired Stokes element: a mesh-robust version of the Scott-Vogelius element

The conforming Scott-Vogelius pair for the stationary Stokes equation in...
03/28/2022

An algebraic preconditioner for the exactly divergence-free discontinuous Galerkin method for Stokes

We present an optimal preconditioner for the exactly divergence-free dis...
01/15/2020

Robust preconditioning of monolithically coupled multiphysics problems

In many applications, one wants to model physical systems consisting of ...