Abstract
In finite element analysis of transient temperature field, it is quite notorious that the numerical solution may quite likely oscillate and/or exceed the reasonable scope, which violates the natural law of heat conduction. For this reason, we put forward the concept of time monotony and spatial monotony, and then derive several sufficient conditions for monotonic solutions in time dimension for 3 - D passive heat conduction equations with a group of finite difference schemes. For some special boundary conditions and regular element meshes, the lower and upper bounds for Δt/Δx2can be obtained from those conditions so that reasonable numerical solutions are guaranteed. Spatial monotony is also discussed. Finally, the lumped mass method is analyzed.
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