CRITERIA OF FINITE ELEMFNT ALGORITHM FOR A CLASS OF PARABOLIC EQUATION

Applied Mathematics and Mechanics (English Edition) ›› 1989, Vol. 10 ›› Issue (12): 1179-1185.

CRITERIA OF FINITE ELEMFNT ALGORITHM FOR A CLASS OF PARABOLIC EQUATION

欧阳华江, 肖丁

Dalian University of Technology, Dalian

收稿日期:1988-10-28 出版日期:1989-12-18 发布日期:1989-12-18

CRITERIA OF FINITE ELEMFNT ALGORITHM FOR A CLASS OF PARABOLIC EQUATION

Ouyang Hua-jiang, Xiao Ding

Dalian University of Technology, Dalian

Received:1988-10-28 Online:1989-12-18 Published:1989-12-18

摘要/Abstract

摘要： 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.

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 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.

欧阳华江;肖丁. CRITERIA OF FINITE ELEMFNT ALGORITHM FOR A CLASS OF PARABOLIC EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 1989, 10(12): 1179-1185.

Ouyang Hua-jiang;Xiao Ding. CRITERIA OF FINITE ELEMFNT ALGORITHM FOR A CLASS OF PARABOLIC EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 1989, 10(12): 1179-1185.

参考文献

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CRITERIA OF FINITE ELEMFNT ALGORITHM FOR A CLASS OF PARABOLIC EQUATION

CRITERIA OF FINITE ELEMFNT ALGORITHM FOR A CLASS OF PARABOLIC EQUATION

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