We study the error induced by the time discretization of a decoupled forwardbackward stochastic differential equations (X,Y,Z). The forward component X is the solution of a Brownian stochastic differential equation and is approximated by a Euler scheme XN with N time steps. The backward component is approximated by a backward scheme. Firstly, we prove that the errors (Y N −Y,ZN −Z) measured in ...

This paper presents two new architectures of cascade ΣΔ modulators that, based on the use of resonation, allow to increase the effective resolution compared to previously reported topologies whereas keeping relaxed output swing and high robustness to non-linearities of the amplifiers. In addition, the use of loop filters based on Forward-Euler integrators, instead of Backward-Euler integrators ...

Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these variational characterizations instead of the partial differential equations themselves, we obtain new schemes with remarkable stability properties. We show that they c...

In this paper we study the stability for all positive time of the fully implicit Euler scheme for the two-dimensional Navier–Stokes equations. More precisely, we consider the time discretization scheme and with the aid of the discrete Gronwall lemma and the discrete uniform Gronwall lemma we prove that the numerical scheme is stable.

Abstract. This paper deals with the formulation of a numerical scheme for solving compressible flow past moving bodies. We use the discontinuos Galerkin finite element method for the space semi-discretization and the Euler backward formula for the time discretization. Moreover, we use ALE mapping for the treatment of a time depended domain and the linearization of inviscid terms using the Vijay...

We consider initial/boundary value problems for the subdiffusion and diffusionwave equations involving a Caputo fractional derivative in time. We develop two fully discrete schemes based on the piecewise linear Galerkin finite element method in space and convolution quadrature in time with the generating function given by the backward Euler method/second-order backward difference method, and es...

In the study of pattern formation in bi–stable systems, the extended Fisher–Kolmogorov (EFK) equation plays an important role. In this paper, some a priori bounds are proved using Lyapunov functional. Further, existence, uniqueness and regularity results for the weak solutions are derived. Using C1-conforming finite element method, optimal error estimates are established for the semidiscrete ca...

Abstract. Variational steepest descent approximation schemes for the modified Patlak-KellerSegel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recov...

A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani, Tucsnak and Weiss [24]. Based on the concept of observers (also called Luenberger observers), this algorithm covers a large class of abstract evolution PDE’s. In this paper, we are concerned with the convergence analysis of this algorithm. More precisely, we provi...

The paper deals with discretisation methods for nonlinear operator equations written as abstract nonlinear evolution equations. Brezis and Pazy showed that the solution of such problems is given by nonlinear semigroups whose theory was founded by Crandall and Liggett. By using the approximation theorem of Brezis and Pazy, we show the N-stability of the abstract nonlinear discrete problem for th...