Displaying similar documents to “Finite volume schemes for fully non-linear elliptic equations in divergence form”

Analysis of an Asymptotic Preserving Scheme for Relaxation Systems

Francis Filbet, Amélie Rambaud (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique


We consider an asymptotic preserving numerical scheme initially proposed by F. Filbet and S. Jin [229 (2010)] and G. Dimarco and L. Pareschi [49 (2011) 2057–2077] in the context of nonlinear and stiff kinetic equations. Here, we propose a convergence analysis of such a scheme for the approximation of a system of transport equations with a nonlinear source term, for which the asymptotic limit is given by a conservation law. We investigate the convergence of the approximate solution ( ...

On Numerical Solution of the Gardner–Ostrovsky Equation

M. A. Obregon, Y. A. Stepanyants (2012)

Mathematical Modelling of Natural Phenomena


A simple explicit numerical scheme is proposed for the solution of the Gardner–Ostrovsky equation ( + + + + ) = which is also known as the extended rotation-modified Korteweg–de Vries (KdV) equation. This equation is used for the description of internal oceanic waves affected by Earth’ rotation. Particular...

Continuity of solutions of a nonlinear elliptic equation

Pierre Bousquet (2013)

ESAIM: Control, Optimisation and Calculus of Variations


We consider a nonlinear elliptic equation of the form div [(∇)] + [] = 0 on a domain Ω, subject to a Dirichlet boundary condition tr = . We do not assume that the higher order term satisfies growth conditions from above. We prove the existence of continuous solutions either when Ω is convex and satisfies a one-sided bounded slope condition, or when is radial: a ( ξ ) = l ( | ξ | ) | ξ | ξ a ( ξ ) = l ( | ξ | ) | ξ | ξ for some increasing:ℝ → ℝ

Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization

Houman Owhadi, Lei Zhang, Leonid Berlyand (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique


We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough ( ) coefficients. Our method does not rely on concepts of ergodicity or scale-separation but on compactness properties of the solution space and a new variational approach to homogenization. The approximation space is generated by an interpolation basis (over scattered points forming a mesh of resolution ) minimizing...

Two-scale FEM for homogenization problems

Ana-Maria Matache, Christoph Schwab (2010)

ESAIM: Mathematical Modelling and Numerical Analysis


The convergence of a two-scale FEM for elliptic problems in divergence form with coefficients and geometries oscillating at length scale ε << 1 is analyzed. Full elliptic regularity independent of is shown when the solution is viewed as mapping from the slow into the fast scale. Two-scale FE spaces which are able to resolve the scale of the solution with work independent of and without analytical homogenization are introduced. Robust in error estimates for the two-scale...

Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation

Clément Mouhot, Lorenzo Pareschi, Thomas Rey (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique


Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically ( ) where is the dimension of the velocity space. In this paper, following the ideas introduced in [C. Mouhot and L. Pareschi, 339 (2004) 71–76, C. Mouhot and L. Pareschi, 75 (2006) 1833–1852], we derive fast summation techniques for the evaluation of discrete-velocity schemes which...