A nonparametric statistical model of small di€usion type is compared with its discretization by a stochastic Euler di€erence scheme. It is shown that the discrete and continuous models are asymptotically equivalent in the sense of Le Cam's de®ciency distance for statistical experiments, when the discretization step decreases with the noise intensity . Mathematics Subject Classi®cation (1991): P...

In this talk we consider the finite element discretization of the Immersed Boundary Method (IBM) introduced by Peskin [6] for fluid-structure interaction problems. With respect to the original finite differences discretization the finite element approach can take advantage from the variational formulation in handling the Dirac delta function which takes into account the presence of the structur...

Fully implicit Runge--Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK are not commonly used in practice with large-scale numerical PDEs because of the difficulty solving stage equations. This paper introduces a theoretical algorithmic framework for nonlinear equations that arise from (and discontinuous Galerkin discretiza...

This paper investigates what is the Hausdorff distance between the set of Euler curves of a Lipschitz continuous differential inclusion and the set of Euler curves for the corresponding convexified differential inclusion. It is known that this distance can be estimated by O( √ h), where h is the Euler discretization step. It has been conjectured that, in fact, an estimation O(h) holds. The pape...

This paper deals with a remarkable integrable discretization of the so(3) Euler top introduced by Hirota and Kimura. Such a discretization leads to an explicit map, whose integrability has been understood by finding two independent integrals of motion and a solution in terms of elliptic functions. Our goal is the construction of its Hamiltonian formulation. After giving a simplified and streaml...

The classical buckling problem, studied by Euler himself, is still important in many fields where macroscale or nanoscale structures may fail under compression. impact of discrete atomic structure on the critical load paramount interest, yet physics insufficiently understood. This study combines experiment and theory to solve that enigma: Phonon dispersion relations are at heart both continuous...

An optimal control problem related to the probability of transition between stable states for a thermally driven Ginzburg-Landau equation is considered. The value function for the optimal control problem with a spatial discretization is shown to converge quadratically to the value function for the original problem. This is done by using that the value functions solve similar Hamilton-Jacobi equ...

Article history: Received 23 June 2009 Received in revised form 25 January 2010 Accepted 25 January 2010 Available online 4 February 2010

We present a novel class of high-order space–time finite element schemes for the Poisson–Nernst–Planck (PNP) equations. prove that our are mass conservative, positivity preserving, and unconditionally energy stable any order approximation. To best knowledge, this is first (arbitrarily) accurate PNP equations simultaneously achieve all these three properties. This accomplished via (1) using elem...

We consider the finite element approximation of the Oldroyd-B system of equations, which models a dilute polymeric fluid, in a bounded domain D ⊂ R, d = 2 or 3, subject to no flow boundary conditions. Our schemes are based on approximating the velocity field with continuous piecewise quadratics and either (a) piecewise constants or (b) continuous piecewise linears for the pressure and the symme...