New progress in 1D self-adaptive analysis based on EEP technology: From linearity to nonlinearity

作者：Yuan Si^*; Du Yan; Xing Qin Yan; Ye Kang Sheng

来源：Engineering Mechanics, 2012, 29(SUPPL. 2): 1-8.

DOI：10.6052/j.issn.1000-4750.2012.07.ST01

• Element energy projection
• Error tolerance
• Finite elements
• Linear odes
• Maximum norm
• Nonlinear
• Nonlinear ODEs
• Nonlinear problems
• Numerical example
• ODEs
• Post-processing stages
• Self-adaptive
• Self-adaptive strategy
• Super-convergence

The EEP (Element Energy Projection) method for super-convergence calculation in the post-processing stage of FEM and the self-adaptive strategy based on the EEP technology are fully successful for linear ODEs and hence pave the way for extending to the self-adaptive analysis of nonlinear ODEs. With recent intensive studying, the technology transfer from linearity to nonlinearity in the self-adaptive analysis of 1D problems has successfully been achieved and the present paper gives a brief overview and report about this progress. A new self-adaptive finite element (FE) strategy for nonlinear ODE problems was proposed. In this method, by means of linearization, the existing linear self-adaptive strategy based on the EEP method is incorporated directly into the solution of nonlinear ODEs to avoid constructing super-convergent formulae and the self-adaptive algorism for each specific and individual nonlinear problem. As a result, a general and unified self-adaptive algorism was proposed. The numerical examples show that the proposed method is highly efficient, stable, general and reliable with the results satisfying the user-preset error tolerance by maximum norm, and hence can serve as the core theory and the algorithm of an advanced and efficient FE solver for nonlinear ODEs.

• 出版日期2012
• 单位清华大学