Reversed stability conditions in transient finite element analysis
Numerical methods which introduce artificially unstable modes are discussed. In structural and elastodynamics these result from optimal mass lumping with higher-order elements. In fluid mechanics an additional source of these modes can be a penalty function with alternating signs. These modes yield unstable modal equations; however, they do not necessarily imply unstable transient integration in the presence of algorithmic damping. Stable integration can be achieved by satisfying a stability condition in which the roles of space-step and time-step are reversed. Elatodyamics, the Navier-Stokes equations, and non-Newtonian fluids provide numerical examples.
scientific article; zbMATH DE number 4057140
scientific article