Technical Report 2012-032

Exact Non-Reflecting Boundary Conditions Revisited: Well-Posedness and Stability

Sofia Eriksson and Jan Nordström

October 2012

Exact non-reflecting boundary conditions for an incompletely parabolic system have been studied. It is shown that well-posedness is a fundamental property of the non-reflecting boundary conditions. By using summation by parts operators for the numerical approximation and a weak boundary implementation, energy stability follows automatically. The stability in combination with the high order accuracy results in a reliable, efficient and accurate method. The theory is supported by numerical simulations.

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