Close Search Advanced
Journals
Resources
About Us
Open Access

Convergence and Superconvergence Analysis of Lagrange Rectangular Elements with Any Order on Arbitrary Rectangular Meshes

Convergence and Superconvergence Analysis of Lagrange Rectangular Elements with Any Order on Arbitrary Rectangular Meshes
Preview
Add to basket

Year:    2014

Journal of Computational Mathematics, Vol. 32 (2014), Iss. 2 : pp. 169–182

Abstract

This paper is to study the convergence and superconvergence of rectangular finite elements under anisotropic meshes. By using of the orthogonal expansion method, an anisotropic Lagrange interpolation is presented. The family of Lagrange rectangular elements with all the possible shape function spaces are considered, which cover the Intermediate families, Tensor-product families and Serendipity families. It is shown that the anisotropic interpolation error estimates hold for any order Sobolev norm. We extend the convergence and superconvergence result of rectangular finite elements to arbitrary rectangular meshes in a unified way.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1310-FE2

Journal of Computational Mathematics, Vol. 32 (2014), Iss. 2 : pp. 169–182

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Lagrange interpolation Anisotropic error bounds Arbitrary rectangular meshes Orthogonal expansion Superconvergence.

  1. Anisotropic linear triangle finite element approximation for multi-term time-fractional mixed diffusion and diffusion-wave equations with variable coefficient on 2D bounded domain

    Zhao, Yanmin | Wang, Fenling | Hu, Xiaohan | Shi, Zhengguang | Tang, Yifa

    Computers & Mathematics with Applications, Vol. 78 (2019), Iss. 5 P.1705

    https://doi.org/10.1016/j.camwa.2018.11.028 [Citations: 13]

  2. Convergence and superconvergence of a fully-discrete scheme for multi-term time fractional diffusion equations

    Zhao, Yanmin | Zhang, Yadong | Liu, F. | Turner, I. | Tang, Yifa | Anh, V.

    Computers & Mathematics with Applications, Vol. 73 (2017), Iss. 6 P.1087

    https://doi.org/10.1016/j.camwa.2016.05.005 [Citations: 44]

  3. Spatial High Accuracy Analysis of FEM for Two-dimensional Multi-term Time-fractional Diffusion-wave Equations

    Wei, Ya-bing | Zhao, Yan-min | Shi, Zheng-guang | Wang, Fen-ling | Tang, Yi-fa

    Acta Mathematicae Applicatae Sinica, English Series, Vol. 34 (2018), Iss. 4 P.828

    https://doi.org/10.1007/s10255-018-0795-1 [Citations: 5]