# Институт вычислительной математики

и математической геофизики

# The International Conference on Computational Mathematics

ICCM-2004

June, 21-25, 2004
Novosibirsk, Academgorodok

## Abstracts

*Numerical solution of differential and integral equations*

## P-multigrid for hp-discretization of the Euler and Navier-Stokes equations

**Keldysh Institute of Applied Mathematics of RAS (Moscow)**
A two-level iterative algorithm is presented for solution of linear systems of equations arising from higher order discretizations of PDEs. The 2D compressible Euler and
Navier-Stokes equations discretized by FEM on unstructured triangular grids are considered. Steady-state solutions of these nonlinear equations are computed by the implicit time-steping scheme [1]. The two-level algorithm is studied as a solver for the linear systems
Au = b that have to be solved in each time step. Here u
denotes the coefficient vector of unknown solution with respect to a finite element basis, A is the stiffness matrix. The choice of a
FE basis affects numerical solution of linear systems. We investigate convergence rate of the algorithm for the
lagrangean(L) and hierarchical(H) bases, usually exploited in FE
application. In the L-basis each local element function is a
polynomial of the same order p. The H-basis uses the
standard linear element modes which are supplemented hierarchical
polynomials of higher degrees up to p. Computational cost of linear system solution of depends usually on mesh parameter h and polynomial order p of finite elements. To achieve order independent (or weekly dependent) property we elaborate the algorithm, given here. It is presented p-stage of the full hp-multigrid that is under development. The results of numerical experiments for a few problems (convection-diffusion, Euler and Navier-Stokes equations) are given.

1. V. Venkatakrishnan, S. Allmaras, D. Kamenetskii, F. Johnson.
Higher Order Schemes for the Compressible Navier-Stokes
Equations. AIAA-2003-3987 (2003).

2. A.A. Martynov and S.Yu. Medvedev. emph{A robust method of anisotropic grid generation. Grid Generation: theory and applications. Computing Centre RAS, Moscow, 2002,c. 266-275

*Note. Abstracts are published in author's edition*

© 1996-2000, Siberian Branch of Russian Academy of Sciences, Novosibirsk

Last update: 06-Jul-2012 (11:52:06)