98-19   Berichtsreihe des Mathematischen Seminars der Universität Kiel

## Locking-free adaptive mixed finite element methods in linear elasticity

Mixed finite element methods such as PEERS or the BDMS methods are designed to avoid locking for nearly incompressible materials in plane elasticity. In this paper, we establish a robust adaptive mesh-refining algorithm that is rigorously based on a reliable and efficient a~posteriori error estimate. Numerical evidence is provided for the $\lambda$-independence of the constants in the a~posteriori error bounds and for the efficiency of the adaptive mesh-refining algorithm proposed.

Bibliographical note: Comp. Methods Appl. Mech. Engrg (1999)

Keywords: a posteriori error estimates, adaptive algorithm, reliability, mixed finite element method, locking