Adaptive Uzawa algorithm for the Stokes equation

Accelerating the Uzawa Algorithm

The Uzawa algorithm is an iterative method for the solution of saddle-point problems, which arise in many applications, including fluid dynamics. Viewing the Uzawa algorithm as a fixedpoint iteration, we explore the use of Anderson acceleration (also knownas Anderson mixing) to improve the convergence. We compare the performance of the preconditioned Uzawa algorithm with and without acceleratio...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

An Adaptive Uzawa FEM for the Stokes Problem: Convergence without the Inf-Sup Condition

We introduce and study an adaptive finite element method (FEM) for the Stokes system based on an Uzawa outer iteration to update the pressure and an elliptic adaptive inner iteration for velocity. We show linear convergence in terms of the outer iteration counter for the pairs of spaces consisting of continuous finite elements of degree k for velocity, whereas for pressure the elements can be e...

A Convergent Adaptive Uzawa Finite Element Method for the Nonlinear Stokes Problem

Analysis of an adaptive Uzawa finite element method for the nonlinear Stokes problem

We design and study an adaptive algorithm for the numerical solution of the stationary nonlinear Stokes problem. The algorithm can be interpreted as a disturbed steepest descent method, which generalizes Uzawa’s method to the nonlinear case. The outer iteration for the pressure is a descent method with fixed step-size. The inner iteration for the velocity consists of an approximate solution of ...