Second-order Hyperbolic C ~ 0 Finite Element Structures And Their Superconvergence,

In this paper, we construct C0 finite elements for second-order ordinary differential equations and second-order hyperbolic equations in time, and at the nodes and some characteristic points several new superconvergence results are derived.This paper is divided in three parts.Part 1 We consider the following second-order ordinary differential equationwith a, b, f sufficiently smooth.We construct a superapproximation function un and have proved that at the nodes the C?finite element solution uh for the equation has following optimal order superconvergence resultsWe also have proved that at some characteristic points in the elements, both uh and uh have superconvergence results.Part 2 We consider the following second-order hyperbolic equationwith A a uniformly elliptical operator independent of t.In this part we use the tensor product and construct C0 finite elements for the equation in time. let 0=t0