Nonconforming H1-Galerkin mixed finite element method for nonlinear sine-Gordon equations

An H¹-Galerkin mixed finite element approximate scheme is proposed with nonconforming quasi-Wilson element for a class of nonlinear sine-Gordon equations. by use of a special property of quasi-Wilson element, i.e. its consistency error is one order higher than the interpolation error, the corresponding optimal error estimates are derived without the generalized elliptic projection which is necessary for classical error estimates of most finite element methods. The scheme is not necessary to satisfy LBB consistency condition.