Different applications of RRE on nonsymmetric algebraic Riccati equation in transport theory

This paper proposes three different ways of applying a vector extrapolation method to a slow converging vector sequence to accelerate the convergence. The solution of this vector sequence is used to solve an algebraic Riccati equation in transport theory. A numerical example is presented to compare the three applications.

A posteriori error estimation for incompressible viscous fluid with a new boundary condition

This paper describes numerical solutions of incompressible Navier-Stokes equations with a new boundary condition. To solve this problem, we use the discretization by mixed finite element method. We use a vector extrapolation method for computing numerical solutions of the steady-state Navier-Stokes equations. In addition, two types of a posteriori error indicator are introduced and are shown to give global error estimates that are equivalent to the true error. A numerical experiment on the driven cavity flow is given to demonstrate the effectiveness of the vector extrapolation method. We compare the result with the solution from commercial code like ADINA system as well as with values from other simulations.