APPROXIMATION OF NONCONFORMING QUASI-WILSON ELEMENT FOR SINE-GORDON EQUATIONS

In this paper, nonconforming quasi-Wilson finite element approximation to a class of nonlinear sine-Gordan equations is discussed. Based on the known higher accuracy results of bilinear element and different techniques from the existing literature, it is proved that the inner product (del(u - I(h)(1)u), del u(h)) and the consistency error can be estimated as order O(h(2)) in broken H-1 - norm/L-2 - norm when u is an element of H-3(Omega)/H-4(Omega), where I(h)(1)u is the bilinear interpolation of u, v(h) belongs to the quasi-Wilson finite element space. At the same time, the superclose result with order O(h(2)) for semi-discrete scheme under generalized rectangular meshes is derived. Furthermore, a fully-discrete scheme is proposed and the corresponding error estimate of order O(h(2) + tau(2)) is obtained for the rectangular partition when u is an element of H-4 (Omega), which is as same as that of the bilinear element with ADI scheme and one order higher than that of the usual analysis on nonconforming finite elements.