Analysis of a Penalty Method

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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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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Keywords

  • Boundary conditions
  • Penalty method
  • Galerkin finite element methods
  • Transport equations