A Sommerfeld non-reflecting boundary condition for the wave equation in mixed form

Hector Espinoza, Ramon Codina, Santiago Badia

Research output: Contribution to journalArticleResearchpeer-review

24 Citations (Scopus)


In this paper we develop numerical approximations of the wave equation in mixed form supplemented with non-reflecting boundary conditions (NRBCs) of Sommerfeld-type on artificial boundaries for truncated domains. We consider three different variational forms for this problem, depending on the functional space for the solution, in particular, in what refers to the regularity required on artificial boundaries. Then, stabilized finite element methods that can mimic these three functional settings are described. Stability and convergence analyses of these stabilized formulations including the NRBC are presented. Additionally, numerical convergence test are evaluated for various polynomial interpolations, stabilization methods and variational forms. Finally, several benchmark problems are solved to determine the accuracy of these methods in 2D and 3D.

Original languageEnglish
Pages (from-to)122-148
Number of pages27
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 1 Jul 2014
Externally publishedYes


  • Artificial boundary condition
  • Non-reflecting boundary condition
  • Open boundary condition
  • Stabilized finite element methods
  • Variational multi-scale method
  • Wave equation

Cite this