Related papers: Error estimates for structure-preserving discretiz…
The incompressible Hall-magnetohydrodynamics (Hall--MHD) system presents substantial analytical and computational challenges due to its stiff, highly nonlinear Hall term and the strict requirement that the magnetic field remains solenoidal.…
We consider an unregularized optimal control problem subject to the steady-state Navier-Stokes equations. We derive the existence of optimal solutions and prove first- and second-order optimality conditions. To approximate solutions to the…
We present here a general method based on the investigation of the relative energy of the system, that provides an unconditional error estimate for the approximate solution of the barotropic Navier Stokes equations obtained by time and…
In this paper, we present an error estimate of a second-order linearized finite element (FE) method for the 2D Navier-Stokes equations with variable density. In order to get error estimates, we first introduce an equivalent form of the…
In this paper, a novel dual-field structure-preserving mixed finite element discretization for incompressible Hall MHD equations is introduced. The discretization satisfies pointwise conservation of mass, magnetic Gauss's law, and…
We derive error estimates of a finite element method for the approximation of solutions to a seven-fields formulation of a magnetohydrodynamics model, which preserves the energy of the system, and the magnetic and cross helicities on the…
In this work we propose and analyse a structure-preserving approximation of the non-isothermal Cahn-Hilliard-Navier-Stokes system using conforming finite elements in space and implicit time discretisation with convex-concave splitting. The…
A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite…
We design an energy-stable and asymptotic-preserving finite volume scheme for the compressible Euler system. Using the relative energy framework, we establish rigorous error estimates that yield convergence of the numerical solutions in two…
The paper focuses on a new error analysis of a class of mixed FEMs for stationary incompressible magnetohydrodynamics with the standard inf-sup stable velocity-pressure space pairs to Navier-Stokes equations and the N\'ed\'elec's edge…
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 problem is established in the presence of concentration…
A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…
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 highly regular unique strong solution and analyse its global…
Magnetohydrodynamics (MHD) is a continuum level model for conducting fluids subject to external magnetic fields, e.g. plasmas and liquid metals. The efficient and robust solution of the MHD system poses many challenges due to it's…
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…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
A conforming finite element scheme with mixed explicit-implicit time discretization for quasi-incompressible Navier-Stokes-Maxwell-Stefan systems in a bounded domain with periodic boundary conditions is presented. The system consists of the…
This paper focuses on an optimal error analysis of a fully discrete finite element scheme for the Cahn--Hilliard--magnetohydrodynamic (CH-MHD) system. The method use the standard inf-sup stable Taylor--Hood/MINI elements to solve the…
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 improved error estimates are a refined consistency analysis…
We introduce a novel structure-preserving method in order to approximate the compressible ideal Magnetohydrodynamics (MHD) equations. This technique addresses the MHD equations using a non-divergence formulation, where the contributions of…