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We investigate a time-domain Galerkin boundary element method for the wave equation outside a Lipschitz obstacle in an absorbing half-space. A priori estimates are presented for both closed surfaces and screens, and we discuss the relevant…

Numerical Analysis · Mathematics 2018-05-01 Heiko Gimperlein , Zouhair Nezhi , Ernst P. Stephan

This paper presents a multiscale Petrov-Galerkin finite element method for time-harmonic acoustic scattering problems with heterogeneous coefficients in the high-frequency regime. We show that the method is pollution- free also in the case…

Numerical Analysis · Mathematics 2015-12-01 Donald L. Brown , Dietmar Gallistl , Daniel Peterseim

We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-square method is employed to ensure stability of the discrete…

Numerical Analysis · Mathematics 2024-11-25 Biswajit Khara , Kumar Saurabh , Robert Dyja , Anupam Sharma , Baskar Ganapathysubramanian

We introduce a space-time Trefftz discontinuous Galerkin method for the first-order transient acoustic wave equations in arbitrary space dimensions, extending the one dimensional scheme of Kretzschmar et al. (2016, IMA J. Numer. Anal., 36,…

Numerical Analysis · Mathematics 2022-08-29 Andrea Moiola , Ilaria Perugia

In this paper, we introduce and analyze a space-time $p$-adaptive discontinuous Galerkin method for nonlinear acoustics. We first present the underlying mathematical model, which is based on a recently derived formulation involving, in…

Numerical Analysis · Mathematics 2026-02-16 Daniele Corallo , Pascal Lehner , Christian Wieners

We propose a time stepping scheme for the space-time systems obtained from Galerkin time-domain boundary element methods for the wave equation. Based on extrapolation, the method proves stable, becomes exact for increasing degrees of…

Numerical Analysis · Mathematics 2020-03-06 Heiko Gimperlein , David Stark

Stochastic Galerkin finite element method (SGFEM) provides an efficient alternative to traditional sampling methods for the numerical solution of linear elliptic partial differential equations with parametric or random inputs. However,…

Numerical Analysis · Mathematics 2021-02-16 Alex Bespalov , Daniel Loghin , Rawin Youngnoi

The Helmholtz equation with variable wavenumbers is challenging to solve numerically due to the pollution effect, which often results in a huge ill-conditioned linear system. In this paper, we present a high-order wavelet Galerkin method to…

Numerical Analysis · Mathematics 2025-03-25 Bin Han , Michelle Michelle

We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation of parabolic problems with moving domains or interfaces. We…

Numerical Analysis · Mathematics 2023-01-23 Santiago Badia , Hridya Dilip , Francesc Verdugo

We present a fully discrete scheme for the numerical approximation of a moving-boundary problem describing diffusants penetration into rubber. Our scheme utilizes the Galerkin finite element method for the space discretization combined with…

Numerical Analysis · Mathematics 2023-12-05 Surendra Nepal , Yosief Wondmagegne , Adrian Muntean

In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method…

Numerical Analysis · Mathematics 2026-05-08 Siyu Cen , Bangti Jin , Yavar Kian , Zhi Zhou

Transverse magnetic (TM) scattering of an electromagnetic wave from a periodic dielectric diffraction grating can mathematically be described by a volume integral equation. This volume integral equation, however, in general fails to feature…

Numerical Analysis · Mathematics 2012-11-19 Armin Lechleiter , Dinh Liem Nguyen

We show how a Trefftz Discontinuous Galerkin (TDG) method for the displacement form of the Helmholtz equation can be used to approximate problems having a generalized impedance boundary condition (GIBC) involving surface derivatives of the…

Numerical Analysis · Mathematics 2018-05-17 Shelvean Kapita , Peter Monk , Virginia Selgas

A semidiscrete Galerkin finite element method applied to time-fractional diffusion equations with time-space dependent diffusivity on bounded convex spatial domains will be studied. The main focus is on achieving optimal error results with…

Numerical Analysis · Mathematics 2020-06-12 Kassem Mustapha

We introduce an $hp$-version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new method is that, while offering arbitrary order convergence rates, it may be implemented…

Numerical Analysis · Mathematics 2024-07-18 Paul Houston , Matthew E. Hubbard , Thomas J. Radley , Oliver J. Sutton , Richard S. J. Widdowson

This paper proposes an isogeometric boundary element method (IGBEM) to solve the electromagnetic scattering problems for three-dimensional doubly-periodic multi-layered structures. The main concerns are the constructions of (i) an open…

Numerical Analysis · Mathematics 2021-10-28 Toru Takahashi , Tetsuro Hirai , Hiroshi Isakari , Toshiro Matsumoto

The functional distributions of particle trajectories have wide applications, including the occupation time in half-space, the first passage time, and the maximal displacement, etc. The models discussed in this paper are for characterizing…

Numerical Analysis · Mathematics 2017-07-27 Zhijiang Zhang , Weihua Deng

We propose a fourth-order unfitted characteristic finite element method to solve the advection-diffusion equation on time-varying domains. Based on a characteristic-Galerkin formulation, our method combines the cubic MARS method for…

Numerical Analysis · Mathematics 2022-06-09 Chuwen Ma , Qinghai Zhang , Weiying Zheng

In outdoor acoustics, the calculations of sound propagating in air can be computationally heavy if the domain is chosen large enough to fulfil the Sommerfeld radiation condition. By strategically truncating the computational domain with a…

This work is concerned with the analysis of a space-time finite element discontinuous Galerkin method on polytopal meshes (XT-PolydG) for the numerical discretization of wave propagation in coupled poroelastic-elastic media. The…

Numerical Analysis · Mathematics 2023-12-05 Paola F. Antonietti , Michele Botti , Ilario Mazzieri