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The acoustic scattering problem is modeled by the exterior Helmholtz equation, which is challenging to solve due to both the unboundedness of the domain and the high dispersion error, known as the pollution effect. We develop high-order…

Numerical Analysis · Mathematics 2026-04-14 Bin Han , Jiwoon Sim

Inverse problems for Partial Differential Equations (PDEs) are crucial in numerous applications such as geophysics, biomedical imaging, and material science, where unknown physical properties must be inferred from indirect measurements. In…

Numerical Analysis · Mathematics 2025-11-12 Dabin Park , Sanghyun Lee , Sunghwan Moon

We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…

Numerical Analysis · Mathematics 2024-11-20 R. H. Drebotiy , H. A. Shynkarenko

We present an a posteriori error estimate based on equilibrated stress reconstructions for the finite element approximation of a unilateral contact problem with weak enforcement of the contact conditions. We start by proving a guaranteed…

Numerical Analysis · Mathematics 2021-09-27 Daniele Antonio Di Pietro , Ilaria Fontana , Kyrylo Kazymyrenko

Investigating the sound field in and around ducts is an important topic in acoustics, e.g. when simulating musical instruments or the human vocal tract. In this paper a method that is based on the boundary element method in 3D combined with…

Numerical Analysis · Mathematics 2022-06-24 Wolfgang Kreuzer

In this paper, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints.…

Numerical Analysis · Mathematics 2021-11-01 Asha K Dond , Thirupathi Gudi , Ramesh Ch. Sau

Consider the scattering of an acoustic plane wave by a bounded elastic obstacle which is immersed in an open space filled with a homogeneous medium. This paper concerns the mathematical analysis of the coupled two- and three-dimensional…

Analysis of PDEs · Mathematics 2018-12-03 Peijun Li , Lei Zhang

The main aim of this article is to analyze mixed finite element method for the second order Dirichlet boundary control problem. Therein, we develop both a priori and a posteriori error analysis using the energy space based approach. We…

Numerical Analysis · Mathematics 2022-07-22 Divay Garg , Kamana Porwal

We develop and analyse residual-based a posteriori error estimates for the virtual element discretisation of a nonlinear stress-assisted diffusion problem in two and three dimensions. The model problem involves a two-way coupling between…

Numerical Analysis · Mathematics 2026-02-26 Franco Dassi , Rekha Khot , Andres E. Rubiano , Ricardo Ruiz-Baier

Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…

Analysis of PDEs · Mathematics 2017-09-07 Peijun Li , Xiaokai Yuan

This paper considers 3-D elastic scattering problems by penetrable obstacles with embedded objects. The well-posedness of transmission problem is proved by employing integral equation method. Then the Inverse Problems , which is to recover…

Analysis of PDEs · Mathematics 2025-12-04 Chun Liu , Jiaqing Yang , Bo Zhang

In this article, we develop a posteriori error analysis of a nonconforming finite element method for a linear quadratic elliptic distributed optimal control problem with two different set of constraints, namely (i) integral state constraint…

Optimization and Control · Mathematics 2021-08-09 Kamana Porwal , Pratibha Shakya

We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods.…

Numerical Analysis · Mathematics 2014-10-23 Simon N. Chandler-Wilde , Stephen Langdon

We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…

Optimization and Control · Mathematics 2025-05-08 Francisco Fuica , Nicolai Jork

We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…

Numerical Analysis · Mathematics 2017-04-24 Alejandro Allendes , Enrique Otarola , Richard Rankin

We develop a fully discrete, semi-implicit mixed finite element method for approximating solutions to a class of fourth-order stochastic partial differential equations (SPDEs) with non-globally Lipschitz and non-monotone nonlinearities,…

Numerical Analysis · Mathematics 2026-02-17 Beniamin Goldys , Agus L. Soenjaya , Thanh Tran

We study the numerical solution of scalar time-harmonic wave equations on unbounded domains which can be split into a bounded interior domain of primary interest and an exterior domain with separable geometry. To compute the solution in the…

Numerical Analysis · Mathematics 2021-06-11 Thorsten Hohage , Christoph Lehrenfeld , Janosch Preuss

In the automotive industry, predicting noise during design cycle is a necessary step. Well-known methods exist to answer this issue in low frequency domain. Among these, Finite Element Methods, adapted to closed domains, are quite easy to…

Computational Engineering, Finance, and Science · Computer Science 2008-12-18 Marianne Viallet , Gérald Poumérol , Olivier Dessombz , Louis Jezequel

The stability and convergence analysis of high-order numerical approximations for the one- and two-dimensional nonlocal wave equations on unbounded spatial domains are considered. We first use the quadrature-based finite difference schemes…

Numerical Analysis · Mathematics 2022-11-09 Jihong Wang , Jerry Zhijian Yang , Jiwei Zhang

We present a novel hybrid numerical-asymptotic boundary element method for high frequency acoustic and electromagnetic scattering by penetrable (dielectric) convex polygons. Our method is based on a standard reformulation of the associated…

Numerical Analysis · Mathematics 2017-12-15 Samuel P. Groth , David P. Hewett , Stephen Langdon