9 citations · 13 across the 15 of their papers we have counts for
15 papers
Error analysis of the Monte Carlo method for compressible magnetohydrodynamics
Eduard Feireisl, Maria Lukacova-Medvidova, Bangwei She +1
We study random compressible viscous magnetohydrodynamic flows. Combining the Monte Carlo method with a deterministic finite volume method we solve the random system numerically. Q…
Estimatable variation neural networks and their application to scalar hyperbolic conservation laws
Mária Lukáčová-Medviďová, Simon Schneider
We introduce estimatable variation neural networks (EVNNs), a class of neural networks that allow a computationally cheap estimate on the norm motivated by the space of…
Error analysis for a viscoelastic phase separation model
Aaron Brunk, Herbert Egger, Oliver Habrich +1
We consider systematic numerical approximation of a viscoelastic phase separation model that describes the demixing of a polymer solvent mixture. An unconditionally stable discreti…
Robust a posteriori error control for the Allen-Cahn equation with variable mobility
Aaron Brunk, Jan Giesselmann, Maria Lukacova-Medvidova
In this work, we derive a -robust a posteriori error estimator for finite element approximations of the Allen-Cahn equation with variable non-degenerate mobility. The estimator…
What is a limit of structure-preserving numerical methods for compressible flows?
Maria Lukacova-Medvidova, Bangwei She, Yuhuan Yuan
We present an overview of recent developments on the convergence analysis of numerical methods for inviscid multidimensional compressible flows that preserve underlying physical st…
Convergence of numerical methods for the Navier-Stokes-Fourier system driven by uncertain initial/boundary data
Eduard Feireisl, Maria Lukacova-Medvidova, Bangwei She +1
We consider the Navier-Stokes-Fourier system governing the motion of a general compressible, heat conducting, Newtonian fluid driven by random initial/boundary data. Convergence of…
Convergence of a generalized Riemann problem scheme for the Burgers equation
Maria Lukacova-Medvidova, Yuhuan Yuan
In this paper we study the convergence of a second order finite volume approximation of the scalar conservation law. This scheme is based on the generalized Riemann problem (GRP) s…
New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties
Alina Chertock, Michael Herty, Arsen S. Iskhakov +3
In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realize…
Penalty method for the Navier-Stokes-Fourier system with Dirichlet boundary conditions: convergence and error estimates
Maria Lukacova-Medvidova, Bangwei She, Yuhuan Yuan
We study the convergence and error estimates of a finite volume method for the compressible Navier-Stokes-Fourier system with Dirichlet boundary conditions. Physical fluid domain i…
Fundamentals of the Oldroyd-B model revisited: Tensorial vs. vectorial theory
Aaron Brunk, Joydip Chaudhuri, Maria Lukacova-Medvidova +1
The standard derivation of the Oldroyd-B model starts from a coupled system of the momentum equation for the macroscopic flow on the one hand, and Fokker-Planck dynamics for molecu…
Convergence analysis of the Monte Carlo method for random Navier--Stokes--Fourier system
Maria Lukacova -- Medvidova, Bangwei She, Yuhuan Yuan
In the present paper we consider the initial data, external force, viscosity coefficients, and heat conductivity coefficient as random data for the compressible Navier--Stokes--Fou…
Statistical solutions for the Navier-Stokes-Fourier system
Eduard Feireisl, Maria Lukacova-Medvidova
We show a general stability result in the framework of strong solutions of the Navier-Stokes-Fourier system describing the motion of a compressible viscous and heat conducting gas.…
Error estimates of a finite volume method for the compressible Navier--Stokes--Fourier system
Danica Basaric, Maria Lukacova-Medvidova, Hana Mizerova +2
In this paper we study the convergence rate of a finite volume approximation of the compressible Navier--Stokes--Fourier system. To this end we first show the local existence of a…
A second-order fully-balanced structure-preserving variational discretization scheme for the Cahn-Hilliard Navier-Stokes system
Aaron Brunk, Herbert Egger, Oliver Habrich +1
We propose and analyze a structure-preserving space-time variational discretization method for the Cahn-Hilliard-Navier-Stokes system. Uniqueness and stability for the discrete pro…
Existence and uniqueness of global classical solutions to a two species cancer invasion haptotaxis model
Jan Giesselmann, Niklas Kolbe, Maria Lukacova-Medvidova +1
We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families, migrate on the extracellular matrix and proliferate. Moreover the model de…