arXiv subjects

Radim Hošek

Publications and source records attributed to Radim Hošek.

3 recordsLinked to original sources

arXiv2017

Weak-Strong Uniqueness for Navier-Stokes/Allen-Cahn system

The coupled Navier-Stokes/Allen-Cahn system is a simple model to describe phase separation in two-component systems interacting with an incompressible fluid flow. We demonstrate the \emph{weak-strong uniqueness} result for this system in a bounded domain in three spatial dimensions which implies that when a strong solution exists then a weak solution emanating from the same data coincides with the strong solution on its whole life-span. The proof of given assertion relies on a form of a relative entropy method.

math.AP↗

arXiv2017

Construction and shape optimization of simplicial meshes in $d$-dimensional space

We provide a constructive proof of a face-to-face simplical partition of a d-dimensional space for arbitrary d by generalizing the idea of Sommerville, used to create space-filling tetrahedra out of triangular base, to any dimension. Each step of construction that increases the dimension is determined up to a positive parameter, d-dimensional simplical partition is therefore parametrized by d parameters. We show the shape optimal value of those parameters.

math.MG↗

arXiv2015

Error estimates for a numerical method for the compressible Navier-Stokes system on sufficiently smooth domains

We derive an a priori error estimate for the numerical solution obtained by time and space discretization by the finite volume/finite element method of the barotropic Navier--Stokes equations. The numerical solution on a convenient polyhedral domain approximating a sufficiently smooth bounded domain is compared with an exact solution of the barotropic Navier--Stokes equations with a bounded density. The result is unconditional in the sense that there are no assumed bounds on the numerical solution.

math.NA↗