The Fourth Order Two Point Boundary Value Element Energy Projection Method Of Mathematical Analysis

The finite element method is one of the efficient and common numerical analysis and calculation methods.With the rapid development of the finite element,people increasingly dissatisfied with the finite element method because the accuracy of stresses is much lower than the accuracy of displacements.To improve the accuracy of derivative of the finite element solution became one of the most important research subject recently.In 2004 for second order two-point boundary value problems Professor Yuan proposed the element-energy-projection(EEP) method based on mechanical interpretation.The fundamental idea comes from the strategy in conventional matrix displacement method for skeletal structures and projection theorem in finite element mathematical theory.The numerical examples show high accuracy of the new method.In 2006,Professor Yuan applied the element energy projection method to the finite element computation of fourth order two-point boundary value problems.The numerical examples show that the EEP method also works well for the fourth order problems.In 2007,Dr Zhao Qinghua give the strict mathematical analysis for some of the results.In this thesis we give a mathematical analysis on the element energy projection method for fourth order two-point boundary value equations.Our main results are as follows:1.We proved the O(h^2k-2)(k≥3) super convergence for pointwise recovery displament, and also provided numerical examples to support the result..2.We proved the O(h^2k-2)(k≥3)super convergence for pointwise recovery stress,and also provided numerical examples to support the result.3.We proved the O(h^2k-2)(k≥3)super convergence for pointwise recovery bending moments,and also provided numerical examples to support the result.4.We proved the O(h^2k-3)(k≥3) super convergence for pointwise recovery shear forces, and also provided numerical examples to support the result.