| 摘 要： | In finite element analysis of transient temperature field,it is quite notorious that thenumerical solution may quite likely oscillate and/or exceed the redsonable scope,whichviolates the natural law of heat conduction For this reason,we put forward the concept oftime monotony and spatial monotony and then derive several sufficient conditions formonolonic solutions in time dimension for3-D passive heat conduction equations with agroup of finite difference schemes.For some special boundary conditions and regularelement meshes,the lower and upper bounds for△t/△x~2 can be obtained from thoseconditions so that reasonable numerical solutions are guaranteed.Spatial monotony is alsodiscussed.Finally,the lumped mass method is analyzed.We creatively give several new criteria for the finite element solutions of a class ofparabolic equation represented by heat conduction equation.
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