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 technique...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 - Ih^1u）, △↓vh） 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 Ih^1u is the bilinear interpolation of u, Vh 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.展开更多
文摘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 - Ih^1u）, △↓vh） 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 Ih^1u is the bilinear interpolation of u, Vh 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.
