NODAL ACCURACY IMPROVEMENT AND SUPER-CONVERGENT COMPUTATION IN FEM ANALYSIS OF FEMOL SECOND ORDER ODES

Elements with degree m is used in finite element method (FEM) to solve the second order ordinary differential equations (ODEs) derived from the FEM of lines (FEMOL). The interior displacement of elements generally has a convergence order of m + 1 , while the nodal displacements can achieve a convergence order of 2m . The super-convergence computation using the element energy projection (EEP) method usually has a convergence order of \min (m + 2,2m) , which benefits from the nodal displacements of a higher convergence order but also limits its accuracy by the nodal displacements of elements with lower degrees. In this paper, a modified EEP (M-EEP) method is proposed. With the EEP solution, the nodal displacement accuracy is improved first, and then the interior displacement of elements is recovered, which leads to a modified EEP solution. Numerical experiments show that improved nodal displacements can achieve a convergence order of 2m + 2 , and the interior displacements of elements always have a convergence order of m + 2 without the constraint of order 2m . For linear elements, the interior displacement of M-EEP solution does not have the limitation of second-order convergence from the traditional FEM solution and can achieve the remarkable third-order convergence, equivalent to the convergence order of quadratic elements.