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This paper is concerned with the approximation of linear and nonlinearinitial-boundary-value problems of pseudo-parabolic equations with Dirichlet boundary conditions. They are discretized in space by spectral Galerkin and collocation…

Numerical Analysis · Mathematics 2020-02-26 Eduardo Abreu , Angel Durán

Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…

Computational Engineering, Finance, and Science · Computer Science 2014-10-14 Nicolás Guarín-Zapata , Juan Gómez , Juan Jaramillo

We consider the numerical solution of time-harmonic acoustic scattering by obstacles with uncertain geometries for Dirichlet, Neumann, impedance and transmission boundary conditions. In particular, we aim to quantify diffracted fields…

Numerical Analysis · Mathematics 2020-02-13 Paul Escapil-Inchauspé , Carlos Jerez-Hanckes

A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial…

Numerical Analysis · Mathematics 2022-05-11 Vincenzo Gulizzi , Robert Saye

This paper proposes and analyzes a fully discrete scheme that discretizes space with an ultra-weak local discontinuous Galerkin scheme and time with the Crank--Nicolson method for the nonlinear biharmonic Schr\"odinger equation. We first…

Numerical Analysis · Mathematics 2022-04-15 Lu Zhang

In this paper the numerical solution of non-autonomous semilinear stochastic evolution equations driven by an additive Wiener noise is investigated. We introduce a novel fully discrete numerical approximation that combines a standard…

Numerical Analysis · Mathematics 2019-07-01 Raphael Kruse , Yue Wu

We present and analyse a new conforming space-time Galerkin discretisation of a semi-linear wave equation, based on a variational formulation derived from De Giorgi's elliptic regularisation viewpoint of the wave equation in second-order…

Numerical Analysis · Mathematics 2025-10-22 Lehel Banjai , Emmanuil H. Georgoulis , Brian Hennessy

We study a class of stochastic semilinear damped wave equations driven by additive Wiener noise. Owing to the damping term, under appropriate conditions on the nonlinearity, the solution admits a unique invariant distribution. We apply…

Numerical Analysis · Mathematics 2023-06-27 Ziyi Lei , Charles-Edouard Bréhier , Siqing Gan

Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…

Numerical Analysis · Mathematics 2020-07-20 Heping Dong , Jun Lai , Peijun Li

We consider the Serre system of equations which is a nonlinear dispersive system that models two-way propagation of long waves of not necessarily small amplitude on the surface of an ideal fluid in a channel. We discretize in space the…

Numerical Analysis · Mathematics 2017-01-04 Dimitrios Antonopoulos , Vassilios Dougalis , Dimitrios Mitsotakis

This paper is concerned with the strong approximation of a semi-linear stochastic wave equation with strong damping, driven by additive noise. Based on a spatial discretization performed by a spectral Galerkin method, we introduce a kind of…

Numerical Analysis · Mathematics 2020-08-10 Ruisheng Qi , Xiaojie Wang

The paper proposes a new, conservative fully-discrete scheme for the numerical solution of the regularised shallow water Boussinesq system of equations in the cases of periodic and reflective boundary conditions. The particular system is…

Numerical Analysis · Mathematics 2021-05-12 Dimitrios Mitsotakis , Hendrik Ranocha , David I. Ketcheson , Endre Süli

In this work, we consider the numerical recovery of a spatially dependent diffusion coefficient in a subdiffusion model from distributed observations. The subdiffusion model involves a Caputo fractional derivative of order $\alpha\in(0,1)$…

Numerical Analysis · Mathematics 2021-01-12 Bangti Jin , Zhi Zhou

A fully discrete approximation of the linear stochastic wave equation driven by additive noise is presented. A standard finite element method is used for the spatial discretisation and a stochastic trigonometric scheme for the temporal…

Numerical Analysis · Mathematics 2013-03-05 D. Cohen , S. Larsson , M. Sigg

A novel space-time discretization for the (linear) scalar-valued dissipative wave equation is presented. It is a structured approach, namely, the discretization space is obtained tensorizing the Virtual Element (VE) discretization in space…

Numerical Analysis · Mathematics 2023-08-31 Paola Francesca Antonietti , Francesca Bonizzoni , Marco Verani

This paper proposes and analyzes a full discretization of the exterior transient Stokes problem with Dirichlet boundary conditions. The method is based on a single layer boundary integral representation, using Galerkin semidiscretization in…

Numerical Analysis · Mathematics 2014-10-14 Constantin Bacuta , Matthew E. Hassell , George C. Hsiao , Francisco-Javier Sayas

Maxwell's equations are considered with transparent boundary conditions, for initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The numerical…

Numerical Analysis · Mathematics 2020-10-21 Balázs Kovács , Christian Lubich

This paper develops a class of robust weak Galerkin methods for the stationary incompressible convective Brinkman-Forchheimer equations. The methods adopt piecewise polynomials of degrees $m\ (m\geq1)$ and $m-1$ respectively for the…

Numerical Analysis · Mathematics 2024-01-30 X. J. Wang , X. P. Xie

The generalised eigenfunction expansion method (GEM) and the singularity expansion method (SEM) are applied to solve the canonical problem of wave scattering on an infinite stretched string in the time domain. The GEM, which is shown to be…

Mathematical Physics · Physics 2025-03-28 Ben Wilks , Michael H. Meylan , Fabien Montiel , Sarah Wakes

The homogeneous wave equation is solved by a time-domain boundary element method (BEM) using low-order shape functions for spatial, and the generalised convolution quadrature method (gCQ) by Lopez-Fernandez and Sauter for temporal…

Numerical Analysis · Mathematics 2026-03-26 Martin Schanz , Vibudha Lakshmi Keshava , Herbert de Gersem