Compressible Navier–Stokes equations with potential temperature transport : stability of the strong solution and numerical error estimates
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Abstract
We present a dissipative measure-valued (DMV)-strong uniqueness result for the compressible Navier–Stokes system with potential temperature transport. We show that strong solutions are stable in the class of DMV solutions. More precisely, we prove that a DMV solution coincides with a strong solution emanating from the same initial data as long as the strong solution exists. As an application of the DMV-strong uniqueness principle we derive a priori error estimates for a mixed finite element-finite volume method. The numerical solutions are computed on polyhedral domains that approximate a sufficiently a smooth bounded domain, where the exact solution exists.
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Journal of mathematical fluid mechanics, 25, Springer, Cham (ZG), 2023, https://doi.org/10.1007/s00021-022-00733-z