5 citations · 5 across the 12 of their papers we have counts for
14 papers
Fully Discrete Active Flux Methods for the Euler Equations: Exploring Different Reconstructions and New Multi-Dimensional Evolution Operators
Christiane Helzel, Mária Lukáčová-Medvid'ová, Amelie Porfetye +1
We present new fully discrete Cartesian grid Active Flux methods for the two-dimensional Euler equations of gas dynamics. A key component of these methods is the evolution operator…
Quantum algorithms for Young measures: applications to nonlinear partial differential equations
Shi Jin, Nana Liu, Maria Lukacova-Medvidova +1
Many nonlinear PDEs have singular or oscillatory solutions or may exhibit physical instabilities or uncertainties. This requires a suitable concept of physically relevant generaliz…
Temperature-driven turbulence in compressible fluid flows
Eduard Feireisl, Maria Lukacova-Medvidova, Bangwei She +1
We study the long-time behaviour of the temperature-driven compressible flows. We show that numerical solutions of a structure-preserving finite volume method generate a discrete a…
Lax convergence theorems and error estimates of a finite element method for the incompressible Euler system
Mária Lukáčová-Medviďová, Bangwei She
In this paper, we present convergence theorems for numerical solutions of the incompressible Euler equations. The first result is the Lax-Wendroff-type theorem, while the second ca…
Convergence of a finite volume method to weak solutions for the compressible Navier-Stokes-Fourier system
Eduard Feireisl, Maria Lukacova-Medvidova, Bangwei She +1
We prove strong convergence of an upwind-type finite volume method to a weak solution of the Navier-Stokes-Fourier system with the Dirichlet boundary conditions. The limit solution…
Error analysis of an asymptotic-preserving, energy-stable finite volume method for barotropic Euler equations
Megala Anandan, K. R. Arun, Amogh Krishnamurthy +1
We propose and analyse an energy-stable and asymptotic-preserving finite volume scheme for the compressible Euler system. Using the relative energy framework, we establish rigorous…
Numerical Study of Dissipative Weak Solutions for the Euler Equations of Gas Dynamics
Shaoshuai Chu, Michael Herty, Alexander Kurganov +2
We study dissipative weak (DW) solutions of the Euler equations of gas dynamics using the first-, second-, third-, fifth-, seventh-, and ninth-order local characteristic decomposit…
Random compressible Euler flows
Maria Lukacova-Medvidova, Simon Schneider
We propose a finite volume stochastic collocation method for the random Euler system. We rigorously prove the convergence of random finite volume solutions under the assumption tha…
Hybrid multiscale method for polymer melts: analysis and simulations
Ranajay Datta, Mária Lukáčová-Medviďová, Andreas Schömer +1
We model the flow behaviour of dense melts of flexible and semiflexible ring polymers in the presence of walls using a hybrid multiscale approach. Specifically, we perform molecula…
Well-posedness of the Euler system of gas dynamics
Eduard Feireisl, Maria Lukacova-Medvidova
We propose a new two-step selection criterion applicable to the dissipative measure--valued solutions of the Euler system of gas dynamics. The process consists of a successive maxi…
New Fully Discrete Active Flux Methods with Truly Multi-Dimensional Evolution Operators and WENO Reconstruction
Amelie Porfetye, Zhuyan Tang, Shaoshuai Chu +2
We propose new fully discrete third-order accurate Active Flux and WENO methods based on truly multidimensional evolution operators for the two-dimensional acoustic equations. Buil…
A Locally Divergence-Free Local Characteristic Decomposition Based Path-Conservative Central-Upwind Scheme for Ideal Magnetohydrodynamics
Shaoshuai Chu, Alexander Kurganov, Maria Lukacova-Medvidova +1
We introduce a locally divergence-free local characteristic decomposition based path-conservative central-upwind (LCD-PCCU) scheme for ideal magnetohydrodynamics (MHD) equations. T…
Convergence analysis for a finite volume evolution Galerkin method for multidimensional hyperbolic systems
Mária Lukáčová-Medvidová, Zhuyan Tang, Yuhuan Yuan
We study the convergence of a finite volume method based on the method of bicharacteristics for multidimensional hyperbolic conservation laws. In particular, we concentrate on the…
DMV-strong uniqueness principle for the compressible Navier-Stokes system with potential temperature transport
Mária Lukáčová-Medvid'ová, Andreas Schömer
We establish a DMV-strong uniqueness result for the compressible Navier-Stokes system with potential temperature transport. The concept of generalized, the so-called dissipative me…