Convergence and Superconvergence of a Nonconforming Finite Element on Anisotropic Meshes
نویسندگان
چکیده
The main aim of this paper is to study the error estimates of a nonconforming finite element for general second order problems, in particular, the superconvergence properties under anisotropic meshes. Some extrapolation results on rectangular meshes are also discussed. Finally, numerical results are presented, which coincides with our theoretical analysis perfectly.
منابع مشابه
A New Superconvergence Property of Wilson Nonconforming Finite Element
In this paper the Wilson nonconforming nite element method is considered to solve the general two-dimensional second-order elliptic boundary value problems. A new superconvergence property at the vertices and the midpoints of four edges of rectangular meshes is obtained. The Wilson nonconforming nite element has been widely used in computational mechanics and structural engineering because of i...
متن کاملLow Order Crouzeix-raviart Type Nonconforming Finite Element Methods for Approximating Maxwell’s Equations
The aim of this paper is to study the convergence analysis of three low order Crouzeix-Raviart type nonconforming rectangular finite elements to Maxwell’s equations, on a mixed finite element scheme and a finite element scheme, respectively. The error estimates are obtained for one of above elements with regular meshes and the other two under anisotropic meshes, which are as same as those in th...
متن کاملHigh accuracy analysis of anisotropic finite element method for a class of nonlinear degenerate wave equation
The convergence analysis of the bilinear finite element method to a class of non-linear degenerate wave equation on anisotropic meshes is considered in this paper. Moreover, the global superconvergence for semidiscrete scheme is proposed through interpolation instead of the Ritz Volterra projection of the exact solution.
متن کاملConvergence of the Nonconforming Wilson Element for a Class of Nonlinear Parabolic Problems
This paper deals with the convergence properties of the nonconforming quadrilateral Wilson element for a class of nonlinear parabolic problems in two space dimensions. Optimal H and L2 error estimates for the continuous time Galerkin approximations are derived. It is also shown for rectangular meshes that the gradient of the Wilson element solution possesses superconvergence, and that the Lx er...
متن کاملNonconforming Wilson Element for a Class of Nonlinear Parabolic Problems
This paper deals with the convergence properties of the nonconforming quadrilateral Wilson element for a class of nonlinear parabolic problems in two space dimensions. Optimal H and L2 error estimates for the continuous time Galerkin approximations are derived. It is also shown for rectangular meshes that the gradient of the Wilson element solution possesses superconvergence, and that the Lx er...
متن کامل