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A Staggered Discontinuous Galerkin Method for a Class of Nonlinear Elliptic Equations

  • Eric T. ChungEmail author
  • Ming Fai Lam
  • Chi Yeung Lam
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 119)

Abstract

In this paper, we present a staggered discontinuous Galerkin (SDG) method for a class of nonlinear elliptic equations in two dimensions. The SDG methods have some distinctive advantages, including local and global conservations, and optimal convergence. So the SDG methods have been successfully applied to a wide range of problems including Maxwell equations, acoustic wave equation, elastodynamics and incompressible Navier-Stokes equations. Among many advantages of the SDG methods, one can apply a local post-processing technique to the solution, and obtain superconvergence. We will analyze the stability of the method and derive a priori error estimates. We solve the resulting nonlinear system using the Newton’s method, and the numerical results confirm the theoretical rates of convergence and superconvergence.

Keywords

staggered discontinuous Galerkin method nonlinear elliptic equation 

Notes

Acknowledgements

The research of Eric Chung is partially supported by Hong Kong RGC General Research Fund (Project: 14301314).

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsThe Chinese University of Hong KongHong Kong SARPeople’s Republic of China

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