Abstract
This work is concerned with the introduction of reconstruction operators as known from higher order finite volume (FV) schemes into the discontinuous Galerkin (DG) method. This operator constructs higher order piecewise polynomial reconstructions from the lower order DG scheme. The result is the increase in accuracy of the DG scheme which is cheaper than directly using standard DG schemes of very high orders. We discuss the reconstruction operators and their construction, the relation to DG and present numerical experiments which demonstrate the increased accuracy of this approach.
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Kučera, V. (2015). On the Use of Reconstruction Operators in Discontinuous Galerkin Schemes. In: Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M. (eds) Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-319-10705-9_7
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DOI: https://doi.org/10.1007/978-3-319-10705-9_7
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