Journal of Scientific Computing

, Volume 53, Issue 1, pp 3–34 | Cite as

Analysis of a Penalty Method

  • Qingshan ChenEmail author
  • Youngjoon Hong
  • Roger Temam


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.


Boundary conditions Penalty method Galerkin finite element methods Transport equations 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Scientific ComputingFlorida State UniversityTallahasseeUSA
  2. 2.Institute for Scientific Computing and Applied MathematicsIndiana UniversityBloomingtonUSA

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