134 citations · 1.1k across the 79 of their papers we have counts for
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math.NA2017★ 41 cited
Generalised Summation-by-Parts Operators and Variable Coefficients
Hendrik Ranocha
High-order methods for conservation laws can be highly efficient if their stability is ensured. A suitable means mimicking estimates of the continuous level is provided by summatio…
math.NA2017★ 34 cited
Stability of Correction Procedure via Reconstruction With Summation-by-Parts Operators for Burgers' Equation Using a Polynomial Chaos Approach
Philipp Öffner, Jan Glaubitz, Hendrik Ranocha
In this paper, we consider Burgers' equation with uncertain boundary and initial conditions. The polynomial chaos (PC) approach yields a hyperbolic system of deterministic equation…
math.NA2017★ 73 cited
Comparison of some Entropy Conservative Numerical Fluxes for the Euler Equations
Hendrik Ranocha
Entropy conservation and stability of numerical methods in gas dynamics have received much interest. Entropy conservative numerical fluxes can be used as ingredients in two kinds o…