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The article begins with a quantitative version of the martingale central limit theorem, in terms of the Kantorovich distance. This result is then used in the study of the homogenization of discrete parabolic equations with random i.i.d. coefficients. For s ...
We complete the picture of sharp eigenvalue estimates for the -Laplacian on a compact manifold by providing sharp estimates on the first nonzero eigenvalue of the nonlinear operator when the Ricci curvature is bounded from below by a negative constant. We ...
In this paper we propose a local orthogonal decomposition method (LOD) for elliptic partial differential equations with inhomogeneous Dirichlet and Neumann boundary conditions. For this purpose, we present new boundary correctors which preserve the common ...
This project aims to study the concept of collocation method for isogeometric analysis with NURBS. We first introduce the isogeometric concept and its main advantages compared to finite elements methods. We then present the isogeometric collocation method ...
A new multiscale coupling method is proposed for elliptic problems with highly oscillatory coefficients with a continuum of scales in a subset of the computational domain and scale separation in complementary regions of the computational domain. A disconti ...
Criteria for the bifurcation of small solutions of an equation F(lambda,u) = 0 from a line {(lambda,0): lambda is an element of R} of trivial solutions are usually based on properties of the DuF(lambda,0) at the trivial solutions, where the partial derivat ...
Generating matching meshes for problems with complex boundaries is often an intricate process, and the use of non-matching meshes appears as an appealing solution. Yet, enforcing boundary conditions on non-matching meshes is not a straightforward process, ...
Divergence-form operators with stationary random coefficients homogenize over large scales. We investigate the effect of certain perturbations of the medium on the homogenized coefficients. The perturbations considered are rare at the local level, but when ...
In this paper, a finite element error analysis is performed on a class of linear and nonlinear elliptic problems with small uncertain input. Using a perturbation approach, the exact (random) solution is expanded up to a certain order with respect to a para ...
We consider a family of degenerate elliptic equations of the form div(del F(del u)) = f, where F is an element of C-1,C-1 is a convex function which is elliptic outside a ball. We prove an excess-decay estimate at points where del u is close to a nondegene ...
