A Dual-Mixed Approximation for a Huber Regularization of the Herschel-Bulkey Flow Problem

04/09/2021
by   Sergio Gonzalez-Andrade, et al.
0

In this paper, we extend a dual-mixed formulation for a nonlinear generalized Stokes problem to a Huber regularization of the Herschel-Bulkey flow problem. The present approach is based on a two-fold saddle point nonlinear operator equation for the corresponding weak formulation. We provide the uniqueness of solutions for the continuous formulation and propose a discrete scheme based on Arnold-Falk-Winther finite elements. The discretization scheme yields a system of Newton differentiable nonlinear equations, for which a semismooth Newton algorithm is proposed and implemented. Local superlinear convergence of the method is also proved. Finally, we perform several numerical experiments to investigate the behavior and efficiency of the method.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 17

page 18

page 20

page 21

page 22

10/13/2019

A Banach space mixed formulation for the unsteady Brinkman-Forchheimer equations

We propose and analyze a mixed formulation for the Brinkman-Forchheimer ...
11/01/2019

Convergence of a damped Newton's method for discrete Monge-Ampere functions with a prescribed asymptotic cone

We prove the convergence of a damped Newton's method for the nonlinear s...
04/06/2020

A BDF2-Semismooth Newton Algorithm for the Numerical Solution of the Bingham Flow with Temperature Dependent Parameters

This paper is devoted to the numerical solution of the non-isothermal in...
05/30/2020

Critical Point Calculations by Numerical Inversion of Functions

In this work, we propose a new approach to the problem of critical point...
03/31/2021

Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning

Substructured domain decomposition (DD) methods have been extensively st...
06/07/2015

Well-posedness of a nonlinear integro-differential problem and its rearranged formulation

We study the existence and uniqueness of solutions of a nonlinear integr...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.