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Analysis of a Penalty Method

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Abstract

In this article we study the simplest one-dimensional transport equation u t +au x =f and study the implementation of the boundary condition using a penalty method combined with a P1 finite element discretization. We discuss the convergence of the method when both the penalty parameter ϵ and the mesh size h go to zero, in sequence or simultaneously. Some numerical simulations are reported also showing the efficiency of the method. Numerical simulations are also made for the similar problem in space dimension 2.

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Authors and Affiliations

  1. Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306, USA

    Qingshan Chen

  2. Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN, 47405, USA

    Youngjoon Hong & Roger Temam

Authors
  1. Qingshan Chen
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  2. Youngjoon Hong
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  3. Roger Temam
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Correspondence to Qingshan Chen.

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Chen, Q., Hong, Y. & Temam, R. Analysis of a Penalty Method. J Sci Comput 53, 3–34 (2012). https://doi.org/10.1007/s10915-011-9553-8

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  • DOI: https://doi.org/10.1007/s10915-011-9553-8

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