A p-TYPE SUPERCONVERGENT RECOVERY METHOD FOR FE ANALYSIS ON BOUNDARY VALUE PROBLEMS OF SECOND-ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

It presents a p-type superconvergent recovery method for the finite element analysis on two-point boundary value problems (BVPs) of second-order nonlinear ordinary differential equations. Based on the superconvergence property of nodal values, a linear two-point BVP which approximately governs the solutions on each element is set up by setting the elements' end values in FE solutions as boundary conditions and linearizing the governing differential equations via Taylor expansion technique. This local linear BVP is solved by using a higher order element from which the solution on each element is recovered. This method is a post-processing approach and the recovery computation is carried out on each element separately. It can improve the accuracy and convergence rate of the solutions significantly with a small computation. Numerical examples demonstrate that this method is efficient, reliable and potential.