Ouyang Hua-jiang, Xiao Ding. Criteria of Finite Element Algorithm for a Class of Parabolic Equation[J]. Applied Mathematics and Mechanics, 1989, 10(12): 1115-1121.
 Citation: Ouyang Hua-jiang, Xiao Ding. Criteria of Finite Element Algorithm for a Class of Parabolic Equation[J]. Applied Mathematics and Mechanics, 1989, 10(12): 1115-1121.

# Criteria of Finite Element Algorithm for a Class of Parabolic Equation

• Publish Date: 1989-12-15
• 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 lime monotony and spatial monotony, and then derive several sufficient conditions for nionotonic solutions in lime dimension for 3-D passive heal 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/Δx2 can be obtained from those conditions so that reasonable numerical solutions are guaranteed. Spatial monotony is also discussed. Finally, the lumped mass method is analyzed.We creatively give several new criteria for the finite element solutions of a class of parabolic equation represented by heal conduction equation.
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