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An Asymptotic Preserving Method for Linear Systems of Balance Laws Based on Galerkin’s Method

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Abstract

We apply the concept of asymptotic preserving schemes (SIAM J Sci Comput 21:441–454, 1999) to the linearized \(p\)-system and discretize the resulting elliptic equation using standard continuous Finite Elements instead of Finite Differences. The fully discrete method is analyzed with respect to consistency, and we compare it numerically with more traditional methods such as Implicit Euler’s method.

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Acknowledgments

I am thankful for fruitful discussions with Sebastian Noelle. Furthermore, I highly appreciate the careful reading and critical annotations from the anonymous reviewer which really helped me to improve the presentation in this paper.

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  1. Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Templergraben 55, 52062 , Aachen, Germany

    Jochen Schütz

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  1. Jochen Schütz
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Correspondence to Jochen Schütz.

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Schütz, J. An Asymptotic Preserving Method for Linear Systems of Balance Laws Based on Galerkin’s Method. J Sci Comput 60, 438–456 (2014). https://doi.org/10.1007/s10915-013-9801-1

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