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We investigate stochastic averaging theory for locally Lipschitz discrete-time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete-time stochastic extremum seeking algorithms. Firstly, by…

Optimization and Control · Mathematics 2015-02-18 Shu-Jun Liu , Miroslav Krstic

We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…

Numerical Analysis · Mathematics 2020-11-09 Per Ljung , Axel Målqvist , Anna Persson

In this paper we establish best approximation type error estimates for the fully discrete Galerkin solutions of the time-dependent Stokes problem using the stream-function formulation. For the time discretization we use the discontinuous…

Numerical Analysis · Mathematics 2026-05-20 Dmitriy Leykekhman , Boris Vexler , Jakob Wagner

In this paper we analyze the finite element approximation of the Stokes equations with non-smooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard…

Numerical Analysis · Mathematics 2019-12-12 Ricardo G. Durán , Lucia Gastaldi , Ariel L. Lombardi

We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using…

Numerical Analysis · Mathematics 2023-04-12 Morgan Görtz , Per Ljung , Axel Målqvist

We consider a finite dimensional approximation of the stochastic nonlinear Schr\"odinger equation driven by multiplicative noise, which is derived by applying a symplectic method to the original equation in spatial direction. Both the…

Numerical Analysis · Mathematics 2016-11-29 Jialin Hong , Xu Wang , Liying Zhang

Locally refined meshes impose severe stability constraints on explicit time-stepping methods for the numerical simulation of time dependent wave phenomena. Local time-stepping methods overcome that bottleneck by using smaller time-steps…

Numerical Analysis · Mathematics 2012-10-19 Marcus Grote , Teodora Mitkova

Consider the scattering of an elastic plane wave by a rigid obstacle, which is immersed in a homogeneous and isotropic elastic medium in two dimensions. Based on a Dirichlet-to-Neumann (DtN) operator, an exact transparent boundary condition…

Numerical Analysis · Mathematics 2019-03-11 Peijun Li , Xiaokai Yuan

This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise under more relaxed conditions. The SPDE is discretized…

Numerical Analysis · Mathematics 2020-01-01 Antoine Tambue , Jean Daniel Mukam

We present a novel space-time isogeometric discretization of the acoustic wave equation in second-order formulation that is intrinsically unconditionally stable. The method relies on a variational framework inspired by [Walkington 2014],…

Numerical Analysis · Mathematics 2025-06-19 Matteo Ferrari , Ilaria Perugia

We consider an initial- and Dirichlet boundary- value problem for a linear Cahn-Hilliard-Cook equation, in one space dimension, forced by the space derivative of a space-time white noise. First, we propose an approximate regularized…

Numerical Analysis · Mathematics 2012-05-22 Georgios T. Kossioris , Georgios E. Zouraris

We introduce a new formulation for the finite element immersed boundary method which makes use of a distributed Lagrange multiplier. We prove that a full discretization of our model, based on a semi-implicit time advancing scheme, is…

Numerical Analysis · Mathematics 2015-03-05 Daniele Boffi , Nicola Cavallini , Lucia Gastaldi

In this paper, we analyze a scheme for the time-dependent variable density Navier-Stokes equations. The algorithm is implicit in time, and the space approximation is based on a low-order staggered non-conforming finite element, the…

Numerical Analysis · Mathematics 2017-07-06 Jean-Claude Latché , Khaled Saleh

We present an abstract framework to study weak convergence of numerical approximations of linear stochastic partial differential equations driven by additive L\'evy noise. We first derive a representation formula for the error which we then…

Probability · Mathematics 2016-02-25 Mihály Kovács , Felix Lindner , René L. Schilling

We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isochoric flows of colloidal suspensions. The symmetric velocity…

Numerical Analysis · Mathematics 2021-08-09 Andrea Bonito , Vivette Girault , Diane Guignard , Kumbakonam R. Rajagopal , Endre Süli

We propose and analyze a non-iterative domain decomposition integrator for the linear acoustic wave equation. The core idea is to combine an implicit Crank-Nicolson step on spatial subdomains with a local prediction step at the subdomain…

Numerical Analysis · Mathematics 2026-04-10 Tim Buchholz , Marlis Hochbruck

A parameter estimation problem is considered for a one-dimensional stochastic wave equation driven by additive space-time Gaussian white noise. The estimator is of spectral type and utilizes a finite number of the spatial Fourier…

Probability · Mathematics 2008-10-02 W. Liu , S. V. Lototsky

Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…

Statistics Theory · Mathematics 2019-11-26 Florian Hildebrandt , Mathias Trabs

We propose and analyse a new type of fully discrete surface finite element approximation of a class of linear parabolic stochastic evolution equations with additive noise. Our discretization uses a surface finite element approximation of…

Numerical Analysis · Mathematics 2025-10-10 Øyvind Stormark Auestad , Geir-Arne Fuglstad , Annika Lang

This paper develops and analyzes some fully discrete mixed finite element methods for the stochastic Cahn-Hilliard equation with gradient-type multiplicative noise that is white in time and correlated in space. The stochastic Cahn-Hilliard…

Numerical Analysis · Mathematics 2019-03-14 Xiaobing Feng , Yukun Li , Yi Zhang