12 citations · 47 across the 18 of their papers we have counts for
19 papers
Maximal dissipation and well-posedness of the Euler system of gas dynamics
Eduard Feireisl, Ansgar Jüngel, Mária Lukáčová-Medvid'ová
We show that any dissipative (measure-valued) solution of the compressible Euler system that complies with Dafermos' criterion of maximal dissipation is necessarily an admissible w…
Convergence and error analysis of compressible fluid flows with random data: Monte Carlo method
Eduard Feireisl, Mária Lukáčová - Medviďová, Bangwei She +1
The goal of this paper is to study convergence and error estimates of the Monte Carlo method for the Navier-Stokes equations with random data. To discretize in space and time, the…
Improved error estimates for the finite volume and the MAC schemes for the compressible Navier-Stokes system
Eduard Feireisl, Mária Lukáčová-Medviďová, Bangwei She
We present new error estimates for the finite volume and finite difference methods applied to the compressible Navier-Stokes equations. The main innovative ingredients of the impro…
Stochastic Galerkin method for cloud simulation. Part II: a fully random Navier-Stokes-cloud model
A. Chertock, A. Kurganov, M. Lukáčová-Medviďová +2
This paper is a continuation of the work presented in [Chertock et al., Math. Cli. Weather Forecast. 5, 1 (2019), 65--106]. We study uncertainty propagation in warm cloud dynamics…
Convergence of Discontinuous Galerkin Schemes for the Euler Equations via Dissipative Weak Solutions
Mária Lukácová-Medvidová, Philipp Öffner
In this paper, we present convergence analysis of high-order finite element based methods, in particular, we focus on a discontinuous Galerkin scheme using summation-by-parts opera…
Penalization method for the Navier-Stokes-Fourier system
Danica Basarić, Eduard Feireisl, Mária Lukáčová-Medviďová +2
We apply the method of penalization to the Dirichlet problem for the Navier-Stokes-Fourier system governing the motion of a general viscous compressible fluid confined to a bounded…
Error estimates of the Godunov method for the multidimensional compressible Euler system
Mária Lukáčová-Medviďová, Bangwei She, Yuhuan Yuan
We derive a priori error of the Godunov method for the multidimensional Euler system of gas dynamics. To this end we apply the relative energy principle and estimate the distance b…
Convergence of first-order Finite Volume Method based on Exact Riemann Solver for the Complete Compressible Euler Equations
Mária Lukáčová-Medviďová, Yuhuan Yuan
Recently developed concept of dissipative measure-valued solution for compressible flows is a suitable tool to describe oscillations and singularities possibly developed in solutio…
Relative energy and weak-strong uniqueness of the two-phase viscoelastic phase separation model
Aaron Brunk, Maria Lukacova-Medvidova
The aim of this paper is to analyze a viscoelastic phase separation model. We derive a suitable notion of the relative energy taking into account the non-convex nature of the energ…
Relative energy estimates for the Cahn-Hilliard equation with concentration dependent mobility
Aaron Brunk, Herbert Egger, Oliver Habrich +1
Based on relative energy estimates, we study the stability of solutions to the Cahn-Hilliard equation with concentration dependent mobility with respect to perturbations. As a by-p…
Existence, regularity and weak-strong uniqueness for the three-dimensional Peterlin viscoelastic model
Aaron Brunk, Yong Lu, Maria Lukacova-Medvidova
In this paper we analyze the three-dimensional Peterlin viscoelastic model. By means of a mixed Galerkin and semigroup approach we prove the existence of a weak solutions. Further…
Global existence of weak solutions to viscoelastic phase separation: Part II Degenerate Case
Aaron Brunk, Maria Lukacova-Medvidova
The aim of this paper is to prove global in time existence of weak solutions for a viscoelastic phase separation. We consider the case with singular potentials and degenerate mobil…
Global existence of weak solutions to viscoelastic phase separation: Part I Regular Case
Aaron Brunk, Maria Lukacova-Medvidova
We prove the existence of weak solutions to a viscoelastic phase separation problem in two space dimensions. The mathematical model consists of a Cahn-Hilliard-type equation for tw…
convergence as a new tool in numerical analysis
Eduard Feireisl, Maria Lukacova-Medvidova, Hana Mizerova
We adapt the concept of convergence of Young measures to the sequences of approximate solutions resulting from numerical schemes. We obtain new results on pointwise c…
On the convergence of a finite volume method for the Navier-Stokes-Fourier system
Eduard Feireisl, Maria Lukacova-Medvidova, Hana Mizerova +1
We study convergence of a finite volume scheme for the Navier-Stokes-Fourier system describing the motion of compressible viscous and heat conducting fluids. The numerical flux use…
Convergence of a finite volume scheme for the compressible Navier--Stokes system
Eduard Feireisl, Maria Lukacova-Medvidova, Hana Mizerova +1
We study convergence of a finite volume scheme for the compressible (barotropic) Navier--Stokes system. First we prove the energy stability and consistency of the scheme and show t…
A finite volume scheme for the Euler system inspired by the two velocities approach
Eduard Feireisl, Maria Lukacova-Medvidova, Hana Mizerova
We propose a new finite volume scheme for the Euler system of gas dynamics motivated by the model proposed by H. Brenner. Numerical viscosity imposed through upwinding acts on the…
Convergence of finite volume schemes for the Euler equations via dissipative measure--valued solutions
Eduard Feireisl, Maria Lukacova-Medvidova, Hana Mizerova
The Cauchy problem for the complete Euler system is in general ill posed in the class of admissible (entropy producing) weak solutions. This suggests there might be sequences of ap…
Numerical simulation of a contractivity based multiscale cancer invasion model
Niklas Kolbe, Maria Lukacova-Medvidova, Nikolaos Sfakianakis +1
We present a problem-suited numerical method for a particularly challenging cancer invasion model. This model is a multiscale haptotaxis advection-reaction-diffusion system that de…