Reversed Stability Conditions in Transient Finite Element Analysis.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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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. Elastodynamics, the Navier-Stokes equations, and non-Newtonian fluids provide numerical examples. Keywords Lumping Mass matrix Trapezoidal method.
- Fluid Mechanics
- Statistics and Probability