Related papers: Convergence of Variational Approximation Schemes f…
In this paper, we develop reliable a posteriori error estimates for numerical approximations of scalar hyperbolic conservation laws in one space dimension. Our methods have no inherent small-data limitations and are a step towards error…
We introduce and study a notion of Asymptotic Preserving schemes, related to convergence in distribution, for a class of slow-fast Stochastic Differential Equations. In some examples, crude schemes fail to capture the correct limiting…
We extend the results about existence of minimizers, relaxation, and approximation proven by Chambolle et al. in 2002 and 2007 for an energy related to epitaxially strained crystalline films, and by Braides, Chambolle, and Solci in 2007 for…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
In this paper we study time semi-discrete approximations of a class of polynomially stable infinite dimensional systems modeling the damped vibrations. We prove that adding a suitable numerical viscosity term in the numerical scheme, one…
The strong convergence of Euler approximations of stochastic delay differential equations is proved under general conditions. The assumptions on drift and diffusion coefficients have been relaxed to include polynomial growth and only…
The convective Allen-Cahn equation has been widely used to simulate multi-phase flows in many phase-field models. As a generalized form of the classic Allen-Cahn equation, the convective Allen-Cahn equation still preserves the maximum bound…
In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve…
This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…
The aim is to assess the combined effect of diffusion and dispersion on shocks in the moderate dispersion regime. For a diffusive dispersive approximation of the equations of one-dimensional elasticity (or p-system), we study convergence of…
We address the formulation and analysis of energy and momentum conserving time integration schemes in the context of particle dynamics, and in particular atomic systems. The article identifies three critical aspects of these models that…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
We present a general framework for the approximation of systems of hyperbolic balance laws. The novelty of the analysis lies in the construction of suitable relaxation systems and the derivation of a delicate estimate on the relative…
This paper develops high-order accurate entropy stable (ES) adaptive moving mesh finite difference schemes for the two- and three-dimensional special relativistic hydrodynamic (RHD) and magnetohydrodynamic (RMHD) equations, which is the…
We introduce novel approximate systems for dispersive and diffusive-dispersive equations with nonlinear fluxes. For purely dispersive equations, we construct a first-order, strictly hyperbolic approximation. Local well-posedness of smooth…
We propose an approximation scheme for a class of semilinear variational inequalities whose Hamiltonian is convex and coercive. The proposed scheme is a natural extension of a previous splitting scheme proposed by Liang, Zariphopoulou and…
We develop the \textit{a posteriori} error analysis of three mixed finite element formulations for rotation-based equations in elasticity, poroelasticity, and interfacial elasticity-poroelasticity. The discretisations use $H^1$-conforming…
We propose novel less diffusive schemes for conservative one- and two-dimensional hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges in the development of accurate and robust numerical methods for the…
In this work, we establish that discontinuous Galerkin methods are capable of producing reliable approximations for a broad class of nonlinear variational problems. In particular, we demonstrate that these schemes provide essential…
In this paper, we derive entropy estimates for a class of schemes for the Euler equations which present the following features: they are based on the internal energy equation (eventually with a positive corrective term at the righ-hand-side…