Abstract:
A novel post-processing super-convergent recovery scheme for one-dimensional
C1 FE is presented, from which super-convergent displacements and forces on the whole domain can be obtained. The scheme is conducted on each element. On each element a local boundary value problem (BVP) is set up by setting the FE solutions of this element's end nodal displacements as essential boundary conditions. Then for each point on this element, a local mesh is set up via dividing the element into two sub-elements by this point and the displacement at this point is recovered from the FE solution of this local BVP on the local mesh with sub-element's degree the same as original element. The displacements at any other points are recovered in the same way. Thus the displacement on the whole domain is recovered. The recovered displacement is continuous and smooth, and from its derivatives the super-convergent rotations, bending moments and shear forces are derived. Numerical examples show that for sufficient smooth solutions with element of degree
m, the convergence order of the recovered displacements and rotations is optimal as
h2m-2, while the order of recovered bending moments and shear forces is
h2m-3 and
h2m-4 respectively, which is (
m-2)-th order higher than those corresponding FE solutions. The proposed post-processing super-convergent recovery scheme is reliable, efficient and potential.