The GAMM Committee for Efficient Numerical Methods for Par tial Differential Equations (GAMM-FachausschuB "Effiziente numerische Verfahren fUr partielle Differenzialgleichungen") organizes conferences and seminars on subjects concerning the algorithmic treatment of partial differential equation prob lems. The first seminar "Efficient Solution of Elliptic Systems" was followed by a second one held at the University of Kiel from January 17th to January 19th, 1986. The title was "Efficient Numerical Methods in Continuum Mechanics." The equations arising in continuum mechanics have many con nections to those of fluid mechanics, but are usually more complex. Therefore, much attention has to be paid to the ef ficient discretization, postprocessing and extrapolation. The seminar was attended by 66 scientists from 10 countries. Most of the 21 lectures presented at the seminar treated the discretization of equations in continuum mechanics by finite elements, methods for improving the accuracy of these approx imations and the use of boundary elements. Other contribu tions presented efficient methods for investigating bifurca tions which play an essential role in practical applications. These proceedings contain 11 contributions in alphabetical order. The editors and organizers of the seminar would like to thank the land Schleswig-Holstein and the DFG (Deutsche Forschungs gemeinschaft) for their support. Kiel, November 1986 W. Hackbusch K. Witsch v Contents Page K. ERIKSSON, C. JOHNSON, J. LENNBLAD: Optimal error estimates and adaptive time and space step control for linear parabolic problems ....................... ."