Abstract
The discontinuous Galerkin (DG) methods[1] have recently become popular for the solution of systems of conservation laws because of their several attractive features such as easy extension to and compact stencil for higher-order (> 2nd) approximation, flexibility in handling arbitrary types of grids for complex geometries, and amenability to parallelization and hp-adaptation. However, the DG Methods have their own share weaknesses. In particular, how to effectively control spurious oscillations in the presence of strong discontinuities, and how to reduce the computing costs and storage requirements for the DGM remain the two most challenging and unresolved issues in the DGM.
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Xia, Y., Frisbey, M., Luo, H. (2015). A Hierarchical WENO Reconstructed Discontinuous Galerkin Method for Computing Shock Waves. In: Bonazza, R., Ranjan, D. (eds) 29th International Symposium on Shock Waves 2. ISSW 2013. Springer, Cham. https://doi.org/10.1007/978-3-319-16838-8_25
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DOI: https://doi.org/10.1007/978-3-319-16838-8_25
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16837-1
Online ISBN: 978-3-319-16838-8
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