Self-Adaptive Strategy for One-Dimensional Finite Element Method Based on EEP Method With Optimal Super-Convergence Order

YUAN Si; XING Qin-yan; WANG Xu; YE Kang-sheng

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Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(5): 533-543

YUAN Si, XING Qin-yan, WANG Xu, YE Kang-sheng. Self-Adaptive Strategy for One-Dimensional Finite Element Method Based on EEP Method With Optimal Super-Convergence Order[J]. Applied Mathematics and Mechanics, 2008, 29(5): 533-543.

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Self-Adaptive Strategy for One-Dimensional Finite Element Method Based on EEP Method With Optimal Super-Convergence Order

Department of Civil Engineering, Tsinghua University; Key Laboratory StructuralEngineering and Vibration of China Education Ministry, Beijing 100084, P. R. China

Received Date: 2008-01-22
Rev Recd Date: 2008-04-02
Publish Date: 2008-05-15

Abstract

Abstract

Based on the newly-developed element energy projection(EEP)method with optimal super-convergence order for computation of super-convergent results,an improved self-adaptive strategy for one-dimensional finite element method(FEM)was proposed.In the strategy,a posteriori errors were estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence,meshes were refined by using error-averaging method,and quasi -FEM solutions were used to replace true FEM solutions in the adaptive process.This strategy has been found to be simple,clear,efficient and reliable.For most of the problems,only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in max-norm.Taking the elliptical ordinary differential equation of second order as the model problem,the fundamental idea,implementation strategy and computational algorithm were described and representative numerical examples were given to show the effectiveness and reliability of the proposed approach.
- finite element method(FEM),
- self-adaptive solution,
- super-convergence,
- optimal convergence order,
- element energy projection,
- condensed shape functions

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References(21)

References

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