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

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016

Part of the book series: Lecture Notes in Computational Science and Engineering ((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.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Mathematics, The Chinese University of Hong Kong, Hong Kong SAR, People’s Republic of China

    Eric T. Chung, Ming Fai Lam & Chi Yeung Lam

Authors
  1. Eric T. Chung
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  2. Ming Fai Lam
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  3. Chi Yeung Lam
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Corresponding author

Correspondence to Eric T. Chung .

Editor information

Editors and Affiliations

  1. School of Mechanical Engineering, University of Campinas, Campinas, Brazil

    Marco L. Bittencourt

  2. Department of Civil Engineering, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil

    Ney A. Dumont

  3. EPFL-SB-MATHICSE-MCSS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Jan S. Hesthaven

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Chung, E.T., Lam, M.F., Lam, C.Y. (2017). A Staggered Discontinuous Galerkin Method for a Class of Nonlinear Elliptic Equations. In: Bittencourt, M., Dumont, N., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016. Lecture Notes in Computational Science and Engineering, vol 119. Springer, Cham. https://doi.org/10.1007/978-3-319-65870-4_42

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