In this paper, we apply EQ rot 1 nonconforming finite element to approximate Signorini problem. If the exact solution u∈H5/2(Ω), the error estimate of order O(h) about the broken energy norm is obtained for quadrilateral meshes satisfying regularity assumption and bi-section condition. Furthermore, the superconvergence results of order O(h3/2) are derived for rectangular meshes. Numerical results are presented to confirm the considered theory.
A highly efficient H1-Galerkin mixed finite element method(MFEM) is presented with linear triangular element for the parabolic integro-differential equation.Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O(h2) for both the original variable u in H1(π) norm and the flux p =u in H(div,π) norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O(h3) are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.
A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.
