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ERROR ESTIMATES FOR A SEMI-DISCRETE MIXED DISCONTINUOUS GALERKIN METHOD WITH AN INTERIOR PENALTY FOR PARABOLIC PROBLEMS

Ohm, Mi Ray;Lee, Hyun Young;Shin, Jun Yong

  • Received : 2016.01.22
  • Accepted : 2016.01.29
  • Published : 2016.01.30

Abstract

In this paper, we consider a semi-discrete mixed discontinuous Galerkin method with an interior penalty to approximate the solution of parabolic problems. We define an auxiliary projection to analyze the error estimate and obtain optimal error estimates in $L^{\infty}(L^2)$ for the primary variable u, optimal error estimates in $L^2(L^2)$ for ut, and suboptimal error estimates in $L^{\infty}(L^2)$ for the flux variable ${\sigma}$.

Keywords

parabolic problems;mixed discontinuous Galerkin method;an interior penalty

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Acknowledgement

Supported by : Kyungsung University