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L 2-error analysis of discontinuous Galerkin approximations for nonlinear Sobolev equations

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Abstract

We apply a discontinuous Galerkin method with symmetric interior penalty terms to approximate the solution of nonlinear Sobolev equations. And we introduce an appropriate elliptic type projection of the solution of a Sobolev equation and prove its optimal convergence. Finally we construct semidiscrete approximations of the solutions of nonlinear Sobolev differential equations, and prove that they converge in L 2 normed space with optimal order of convergence.

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Authors and Affiliations

  1. Division of Information Systems Engineering, Dongseo University, Busan, 617-716, Korea

    Mi Ray Ohm

  2. Department of Mathematics, Kyungsung University, Busan, 608-736, Korea

    Hyun Young Lee

  3. Department of Applied Mathematics, Pukyong National University, Busan, 608-737, Korea

    Jun Yong Shin

Authors
  1. Mi Ray Ohm
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  2. Hyun Young Lee
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  3. Jun Yong Shin
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Corresponding author

Correspondence to Hyun Young Lee.

Additional information

This research was supported by Dongseo Frontier Research Grant in 2009.

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Ohm, M.R., Lee, H.Y. & Shin, J.Y. L 2-error analysis of discontinuous Galerkin approximations for nonlinear Sobolev equations. Japan J. Indust. Appl. Math. 30, 91–110 (2013). https://doi.org/10.1007/s13160-012-0096-7

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  • DOI: https://doi.org/10.1007/s13160-012-0096-7

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