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A modified weak Galerkin finite element methods for convection–diffusion problems in 2D

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Abstract

In this paper, we develop a modified weak Galerkin finite element method on arbitrary grids for convection–diffusion problems in two dimensions based on our previous work (Wang et al., J Comput Appl Math 271, 319–327, 2014), in which we only considered second order Poisson equations and thus only introduced a modified weak gradient operator. This method, called MWG-FEM, is based on a modified weak gradient operator and weak divergence operator which is put forward in this paper. Optimal order error estimates are established for the corresponding MWG-FEM approximations in both a discrete \(H^1\) norm and the standard \(L^2\) norm. Numerical results are presented to demonstrate the robustness, reliability, and accuracy of the MWG-FEM.

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Acknowledgments

The authors would like to sincerely thank Professor Xiu Ye in Arkansas University at Little Rock, USA, for her invaluable suggestions. The first author’s research is partially supported by the Natural Science Foundation of Shandong Province of China Grant ZR2013AM023 and NSAF Grant No. U1430101.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, Shandong, China

    Fuzheng Gao

  2. School of Materials Science and Engineering, Shandong University, Jinan, China

    Fuzheng Gao

  3. Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA

    Xiaoshen Wang

  4. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    Lin Mu

Authors
  1. Fuzheng Gao
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  2. Xiaoshen Wang
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  3. Lin Mu
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Correspondence to Fuzheng Gao.

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Gao, F., Wang, X. & Mu, L. A modified weak Galerkin finite element methods for convection–diffusion problems in 2D. J. Appl. Math. Comput. 49, 493–511 (2015). https://doi.org/10.1007/s12190-014-0850-x

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  • DOI: https://doi.org/10.1007/s12190-014-0850-x

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