Asymptotic Expansion and Superconvergence for Triangular Linear Finite Element on a Class of Typical Mesh
نویسندگان
چکیده
In this paper, we present a new approach to obtain the asymptotic expansion and superconvergence for the linear element on Union Jack mesh. First, we construct a generalized interpolation function and its discrete harmonic extension by using the energy embedding method and the method of separation of variables. Then, we present elaborate estimates for the generalized interpolation function and the harmonic extension. Finally, the asymptotic expansion, superconvergence and extrapolation are obtained based on those estimates.
منابع مشابه
The Discontinuous Galerkin Method for Two-dimensional Hyperbolic Problems Part II: A Posteriori Error Estimation
In this manuscript we construct simple, efficient and asymptotically correct a posteriori error estimates for discontinuous finite element solutions of scalar firstorder hyperbolic partial differential problems on triangular meshes. We explicitly write the basis functions for the error spaces corresponding to several finite element spaces. The leading term of the discretization error on each tr...
متن کاملSuperconvergence and Extrapolation Analysis of a Nonconforming Mixed Finite Element Approximation for Time-Harmonic Maxwell's Equations
In this paper, a nonconforming mixed finite element approximating to the three-dimensional time-harmonic Maxwell’s equations is presented. On a uniform rectangular prism mesh, superclose property is achieved for electric field E and magnetic field H with the boundary condition E × n = 0 by means of the asymptotic expansion. Applying postprocessing operators, a superconvergence result is stated ...
متن کاملA Symmetric Finite Volume Element Scheme on Quadrilateral Grids and Superconvergence
A symmetric finite volume element scheme on quadrilateral grids is established for a class of elliptic problems. The asymptotic error expansion of finite volume element approximation is obtained under rectangle grids, which in turn yields the error estimates and superconvergence of the averaged derivatives. Numerical examples confirm our theoretical analysis.
متن کاملExtrapolation of Mixed Finite Element Approximations for the Maxwell Eigenvalue Problem
In this paper, a general method to derive asymptotic error expansion formulas for the mixed finite element approximations of the Maxwell eigenvalue problem is established. Abstract lemmas for the error of the eigenvalue approximations are obtained. Based on the asymptotic error expansion formulas, the Richardson extrapolation method is employed to improve the accuracy of the approximations for ...
متن کاملSuperconvergence and Extrapolation for Mixed Finite Element Methods on Rectangular Domains
Asymptotic expansions for the RT (Raviart-Thomas) mixed finite element approximation by the lowest-order rectangular element associated with a second-order elliptic equation on a rectangular domain are derived. Superconvergence for the vector field along the Gauss lines is obtained as a result of the expansion. A procedure of postprocessed extrapolation is presented for the scalar field, as wel...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012