This volume contains 23 contributions to the 10th GAMM-Seminar, which was held in Kiel on the 14-16 of January 1994. The central topics are advanced numerical techniques for solving flow problems. The Navier-Stokes equations are discussed with respect to anisotropically refined meshes, in combination with non-equilibrium chemistry and with respect to implicit time-discretizations and parallel solvers. Furthermore, robust multi-grid methods are described for this problem. Five papers are devoted to parallel algorithms, and a further one to domain decomposition techniques. The very important aspect of adaptive strategies is considered in several contributions, including a discussion of appropriate error estimators. Other subjects are the FEM-BEM coupling, convection-dominated systems, unstructured grid techniques and complex geometries in 3-D.

Table of Contents

A hierarchical basis multigrid method for unstructured grids, R.E. Bank and J. Xu; structured adaptive finite-volume multigrid for compressible flows, H.T.M. van der Maarel and P.W. Hemker; on the solution of non-linear equations for non-differentiable mappings, O. Axelsson and I.E. Kaporin; finite element solution of the incompressible Navier-Stokes equations on anisotropically refined meshes, R. Becker and R. Rannacher; downwind numbering - a robust multigrid method for convection-diffusion problems on unstructured grids, J. Bey and G. Wittum; a fast solver for gas flow networks, G. Engl; on the design of piecewise uniform meshes for solving advection-dominated transport equations to a prescribed accuracy, P. A. Farrell et al; numerical simulation of three-dimensional non-stationary compressible flow in complex geometries, M. Geiben; on the numerical simulation of coupled transient problems on MIMD parallel systems, U. Groh et al; fast solvers for coupled FEM-BEM equations I, M. Hahne et al; numerical simulations of compressible Navier-Stokes equations with non-equilibrium chemistry, M. Hilgenstock et al; pre-conditioned cg-like methods and defect correction for solving steady incompressible Navier-Stokes problems, G.H. Juncu; a domain decomposition method for singularly perturbed elliptic problems, A. Kapurkin and G. Lube; a parallel subspace decomposition method for elliptic and hyperbolic systems, E. Katzer; implicit time-discretization of the non-sttionary incompressible Navier-Stokes equations, S. Jueller et al; experiences with a parallel multiblock multigrid solution technique for the Euler equations, C.W. Oosterlee et al; a coupled algebraic multigrid method for the 3-D Navier-Stokes equations. M. Raw; robust multigrid methods for the incompressible Navier-Stokes equations, H. Reichert and G. Wittum; a new robust multigrid methods for 2-D convection-diffusion problems, A. Reusken; adapting meshes by deformation - numerical examples and applications, M. Rumpf; multigrid convergence rates of a sequential and a parallel Navier-Stokes solver, F. Schieweck; parallel iterative solvers for symmetric boundary element domain decomposition methods, O. Steinbach; the equivalence of a posteriori error estimators, R. Verfuerth.