Convergence and error estimates of a penalization finite volume method for the compressible Navier-Stokes system

In numerical simulations a smooth domain occupied by a fluid has to be approximated by a computational domain that typically does not coincide with a physical domain. Consequently, in order to study convergence and error estimates of a numerical method domain-related discretization errors, the so-called variational crimes, need to be taken into account. In this paper we present an elegant alternative to a direct, but rather technical, analysis of variational crimes by means of the penalty approach. We embed the physical domain into a large enough cubed domain and study the convergence of a finite volume method for the corresponding domain-penalized problem. We show that numerical solutions of the penalized problem converge to a generalized, the so-called dissipative weak, solution of the original problem. If a strong solution exists, the dissipative weak solution emanating from the same initial data coincides with the strong solution. In this case, we apply a novel tool of the relative energy and derive the error estimates between the numerical solution and the strong solution. Extensive numerical experiments that confirm theoretical results are presented.


Penalty method for the Navier-Stokes-Fourier system with Dirichlet boundary conditions: convergence and error estimates

We study the convergence and error estimates of a finite volume method f...

Convergence and error analysis of compressible fluid flows with random data: Monte Carlo method

The goal of this paper is to study convergence and error estimates of th...

Analysis of an alternative Navier-Stokes system: Weak entropy solutions and a convergent numerical scheme

We consider an alternative Navier-Stokes model for compressible viscous ...

Progress Report on Numerical Modeling of a Prototype Fuel Cell

Progress on the numerical modeling of a prototype fuel cell is reported....

Error estimates of the Godunov method for the multidimensional compressible Euler system

We derive a priori error of the Godunov method for the multidimensional ...

A Bayesian Conjugate Gradient Method

A fundamental task in numerical computation is the solution of large lin...

A posteriori error estimates for wave maps into spheres

We provide a posteriori error estimates in the energy norm for temporal ...

Please sign up or login with your details

Forgot password? Click here to reset