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.
AnalysisoftheSBP-SATStabilization for Finite Element Methods Part I: Linear problems
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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.
Develops energy-stable asymptotic-preserving discretizations of a hyperbolized Cahn-Hilliard equation via SBP operators and IMEX Runge-Kutta methods guided by relative-energy error estimates.
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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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Justification and structure- and asymptotic-preserving discretizations of a hyperbolized Cahn-Hilliard equation
Develops energy-stable asymptotic-preserving discretizations of a hyperbolized Cahn-Hilliard equation via SBP operators and IMEX Runge-Kutta methods guided by relative-energy error estimates.