Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients

By Ken Mattsson. Journal of Scientific Computing, 2012

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High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains (2013, methodology): “33 to what Mattsson [19] calls compatible operators, M(θ) = DP[θ]D +R(θ), R(θ) = R(θ) , ζR(θ)ζ ≥ 0, ∀ζ, (2.”
Mimetic finite difference method (2014, methodology): “Further developments are found in [201] [252], where the Euler equations are solved using an energy-stable scheme based on the fifth-order summation-by-parts operators.”
Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (2014, methodology): “Finally, using widestencil SBP operators results in the loss of one order of accuracy in the context of parabolic PDEs [32].”