An augmented IIM-level set method for Stokes equations with discontinuous viscosity.
An axisymmetric squeezing fluid flow between the two infinite parallel plates in a porous medium channel.
An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier–Stokes flows
We present the current Reduced Basis framework for the efficient numerical approximation of parametrized steady Navier–Stokes equations. We have extended the existing setting developed in the last decade (see e.g. [S. Deparis, SIAM J. Numer. Anal. 46 (2008) 2039–2067; A. Quarteroni and G. Rozza, Numer. Methods Partial Differ. Equ. 23 (2007) 923–948; K. Veroy and A.T. Patera, Int. J. Numer. Methods Fluids 47 (2005) 773–788]) to more general affine and nonaffine parametrizations (such as volume-based...
An elastohydrodynamic coupled problem between a piezoviscous Reynolds equation and a hinged plate model
An Elliptic Boundary Value problem occurring in Magnetohydrodynamcis.
An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment
We consider the system of partial differential equations governing the one-dimensional flow of two superposed immiscible layers of shallow water. The difficulty in this system comes from the coupling terms involving some derivatives of the unknowns that make the system nonconservative, and eventually nonhyperbolic. Due to these terms, a numerical scheme obtained by performing an arbitrary scheme to each layer, and using time-splitting or other similar techniques leads to instabilities in...
An entropy-correction free solver for non-homogeneous shallow water equations
In this work we introduce an accurate solver for the Shallow Water Equations with source terms. This scheme does not need any kind of entropy correction to avoid instabilities near critical points. The scheme also solves the non-homogeneous case, in such a way that all equilibria are computed at least with second order accuracy. We perform several tests for relevant flows showing the performance of our scheme.
An entropy-correction free solver for non-homogeneous shallow water equations
In this work we introduce an accurate solver for the Shallow Water Equations with source terms. This scheme does not need any kind of entropy correction to avoid instabilities near critical points. The scheme also solves the non-homogeneous case, in such a way that all equilibria are computed at least with second order accuracy. We perform several tests for relevant flows showing the performance of our scheme.
An error estimate for a numerical scheme for the compressible Navier-stokes system
An error estimate for finite volume methods for the Stokes equations.
An error estimate uniform in time for spectral Galerkin approximations for the equations for the motion of a chemical active fluid.
We study error estimates and their convergence rates for approximate solutions of spectral Galerkin type for the equations for the motion of a viscous chemical active fluid in a bounded domain. We find error estimates that are uniform in time and also optimal in the L2-norm and H1-norm. New estimates in the H(-1)-norm are given.
An example in the gradient theory of phase transitions
We prove by giving an example that when the asymptotic behavior of functionals is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case (see [2]) is no longer true in higher dimensions.
An example in the gradient theory of phase transitions
We prove by giving an example that when n ≥ 3 the asymptotic behavior of functionals is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case (see [2]) is no longer true in higher dimensions.
An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit
The purpose of this work is to study an example of low Mach (Froude) number limit of compressible flows when the initial density (height) is almost equal to a function depending on . This allows us to connect the viscous shallow water equation and the viscous lake equations. More precisely, we study this asymptotic with well prepared data in a periodic domain looking at the influence of the variability of the depth. The result concerns weak solutions. In a second part, we discuss the general low...
An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit
The purpose of this work is to study an example of low Mach (Froude) number limit of compressible flows when the initial density (height) is almost equal to a function depending on x. This allows us to connect the viscous shallow water equation and the viscous lake equations. More precisely, we study this asymptotic with well prepared data in a periodic domain looking at the influence of the variability of the depth. The result concerns weak solutions. In a second part, we discuss...
An existence proof for the stationary compressible Stokes problem
In this paper, we prove the existence of a solution for a quite general stationary compressible Stokes problem including, in particular, gravity effects. The Equation Of State gives the pressure as an increasing superlinear function of the density. This existence result is obtained by passing to the limit on the solution of a viscous approximation of the continuity equation.
An existence result for a free boundary shallow water model using a lagrangian scheme
An existence result for partially regular weak solutions of certain abstract evolution equations, with an application to magneto-hydrodynamics.
An explicit right inverse of the divergence operator which is continuous in weighted norms
The existence of a continuous right inverse of the divergence operator in , 1 < p < ∞, is a well known result which is basic in the analysis of the Stokes equations. The object of this paper is to show that the continuity also holds for some weighted norms. Our results are valid for Ω ⊂ ℝⁿ a bounded domain which is star-shaped with respect to a ball B ⊂ Ω. The continuity results are obtained by using an explicit solution of the divergence equation and the classical theory of singular integrals...
An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
In this article, we consider the initial value problem which is obtained after a space discretization (with space step ) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between and the time step size...