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math.NA2026
A well posed and stable canonical evaporation model problem for phase-change in two-phase flows
Jan Nordström
We formulate a well posed interface formulation for canonical one-dimensional evaporation two-phase model problems (the Stefan and Sucking problems) commonly used to validate produ…
math.NA2026
Summation-by-parts operators for general function spaces: optimal nodes
Nicholas Hale, Charis Harley, Prince Nchupang +1
Gauss-Lobatto quadrature nodes and weights are optimal for closed summation-by-parts (SBP) formulations based on polynomial approximation spaces in the sense that for a prescribed…
math.NA2025
Numerical boundary flux functions that give provable bounds for nonlinear initial boundary value problems with open boundaries
Andrew R. Winters, David A. Kopriva, Jan Nordström
We present a strategy for interpreting nonlinear, characteristic-type penalty terms as numerical boundary flux functions that provide provable bounds for solutions to nonlinear hyp…