Local linear instabilities in entropy-stable discretizations cause negligible practical errors because their growth is small, oscillatory, boundary-localized, and suppressible, with no direct extension to nonlinear two-point-flux cases.
Journal of Scientific Computing 85(2), 43 (2020)
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Active Flux/PamPa schemes incorporate discontinuous Galerkin methods as a building block, possess intrinsic bound-preserving properties illustrated numerically, and satisfy the summation-by-parts property in one dimension.
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On the Practical Impact of Local Linear Instabilities in Entropy-Stable Schemes
Local linear instabilities in entropy-stable discretizations cause negligible practical errors because their growth is small, oscillatory, boundary-localized, and suppressible, with no direct extension to nonlinear two-point-flux cases.
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Some new properties of an Active flux type scheme: PamPa
Active Flux/PamPa schemes incorporate discontinuous Galerkin methods as a building block, possess intrinsic bound-preserving properties illustrated numerically, and satisfy the summation-by-parts property in one dimension.