(untitled) (Journal of Computational Mathematics, 2018)
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 (∇(u-I_h^1u),∇ v_h) and the consistency error can be estimated as order O(h^2) in broken H^1-norm/L^2-norm when u ∈ H^3(Ω)/H^4(Ω), where I_h^1u 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+τ^2) is obtained for the rectangular partition when u ∈ H^4(Ω), 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.