scholarly journals A relaxed non-linear inexact Uzawa algorithm for stokes problem

2019 ◽  
Vol 23 (4) ◽  
pp. 2323-2331
Author(s):  
Shao-Qing Zheng ◽  
Jun-Feng Lu
Keyword(s):  
Fluid Dynamics ◽  
Numerical Experiments ◽  
Stokes Problem ◽  
Mixed Finite Element ◽  
Finite Element Approximation ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Element Approximation ◽  
Uzawa Algorithm ◽  
Non Linear

In this paper, we consider a Stokes problem arising in fluid dynamics and thermal science, which can be transformed to a symmetric saddle point problem by using the mixed finite element approximation. A relaxed non-linear inexact Uzawa algorithm is proposed for solving the problem, and the convergence of this algorithm is also considered. Numerical experiments are presented to show the efficiency of relaxed non-linear inexact Uzawa algorithm.

scholarly journals A special parameterized inexact Uzawa algorithm for symmetric saddle point problem

2018 ◽  
Vol 22 (4) ◽  
pp. 1715-1721
Author(s):  
Jun-Feng Lu ◽  
Li Ma
Keyword(s):  
Fluid Dynamics ◽  
Saddle Point ◽  
Numerical Experiments ◽  
Stokes Problem ◽  
Sufficient Conditions ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Uzawa Algorithm ◽  
Special Algorithm

In this paper, we consider a symmetric saddle point problem arising in the fluid dynamics. A special parameterized inexact Uzawa algorithm is proposed for solving the symmetric saddle point problem. The convergence of this special algorithm is considered. Sufficient conditions for the convergence are given. Numerical experiments resulting from stokes problem are presented to show the efficiency of the algorithm.

Easily implementable iterative methods for variational inequalities with nonlinear diffusion–convection operator and constraints to the gradient of solution

2015 ◽  
Vol 30 (1) ◽  
Author(s):  
Erkki Laitinen ◽  
Alexander Lapin ◽  
Sergey Lapin
Keyword(s):  
Variational Inequalities ◽  
Iterative Methods ◽  
Nonlinear Diffusion ◽  
Linear Equations ◽  
Finite Element Approximation ◽  
Iterative Solution ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Element Approximation ◽  
Diffusion Convection

AbstractNew iterative solution methods are proposed for the finite element approximation of a class of variational inequalities with nonlinear diffusion-convection operator and constraints to the gradient of solution. Implementation of every iteration of these methods reduces to the solution of a system of linear equations and a set of two-dimensional minimization problems. Convergence is proved by the application of a general result on the convergence of the iterative methods for a nonlinear constrained saddle point problem.

New Mixed Finite Element Formulations for Transient and Steady State Creep Problems

1989 ◽  
Vol 42 (11S) ◽  
pp. S150-S156
Author(s):  
Abimael F. D. Loula ◽  
Joa˜o Nisan C. Guerreiro
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Mixed Finite Element ◽  
Finite Element Approximation ◽  
Steady State Creep ◽  
Element Approximation ◽  
New Approach ◽  
Finite Element Approximations ◽  
Transient Problems ◽  
Transient And Steady State

We apply the mixed Petrov–Galerkin formulation to construct finite element approximations for transient and steady-state creep problems. With the new approach we recover stability, convergence, and accuracy of some Galerkin unstable approximations. We also present the main results on the numerical analysis and error estimates of the proposed finite element approximation for the steady problem, and discuss the asymptotic behavior of the continuum and discrete transient problems.

A mixed finite-element method for elliptic operators with Wentzell boundary condition

2018 ◽  
Vol 40 (1) ◽  
pp. 87-108
Author(s):  
Eberhard Bänsch ◽  
Markus Gahn
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Mixed Finite Element ◽  
A Priori ◽  
Mixed Finite Element Method ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Weak Formulation ◽  
Wentzell Boundary Condition ◽  
Polyhedral Domain

Abstract In this paper we introduce and analyze a mixed finite-element approach for a coupled bulk-surface problem of second order with a Wentzell boundary condition. The problem is formulated on a domain with a curved smooth boundary. We introduce a mixed formulation that is equivalent to the usual weak formulation. Furthermore, optimal a priori error estimates between the exact solution and the finite-element approximation are derived. To this end, the curved domain is approximated by a polyhedral domain introducing an additional geometrical error that has to be bounded. A computational result confirms the theoretical findings.

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