Self-Adaptive Strategy for One-Dimensional Finite Element Method Based on EEP Method

YUAN Si; HE Xue-feng

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YUAN Si, HE Xue-feng. Self-Adaptive Strategy for One-Dimensional Finite Element Method Based on EEP Method[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1280-1291.

Citation:

YUAN Si, HE Xue-feng. Self-Adaptive Strategy for One-Dimensional Finite Element Method Based on EEP Method[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1280-1291.

Citation:

YUAN Si, HE Xue-feng. Self-Adaptive Strategy for One-Dimensional Finite Element Method Based on EEP Method[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1280-1291.

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Self-Adaptive Strategy for One-Dimensional Finite Element Method Based on EEP Method

Department of Civil Engineering, Tsinghua University, Beijing 100084, P. R. China

Received Date: 2005-10-09
Rev Recd Date: 2006-08-10
Publish Date: 2006-11-15

Abstract

Abstract

Based on the newly-developed element energy projection(EEP)method for computation of super-convergent results in one-dimensional finite element method(FEM),the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation.As a result, a satisfactory FEM mesh can be obtained,and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance.Even though the error tolerance was not completely satisfied,one or two steps of further local refinements would be sufficient.This strategy has been found to be very simple,rapid,cheap and efficient.Taking the elliptical ordinary differential equation of the second order as the model problem,the fundamental idea, implementation strategy and detailed algorithm were described.Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.
- FEM,
- self-adaptive solution,
- super-convergence,
- element energy projection,
- ODE

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References(11)

References

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