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Related Articles from SNS
Fourier--Galerkin Methods for Subwavelength Resonances in two-dimensional Acoustic Metamaterials
arXiv:2605.23251v2 Announce Type: replace Abstract: We present a Fourier--Galerkin asymptotic framework for the analysis and computation of subwavelength resonances in two-dimensional scattering problems in finite domains. Starting from the boundary integral formulation, we apply a Fourier--Galerkin discretization to derive an explicit finite-dimensional effective matrix whose kernel characterizes the resonant frequencies. In the subwavelength regime, we obtain asymptotic expansions of this...
Structure-Preserving Discontinuous Galerkin Methods for Stochastic Shallow Water Equations
arXiv:2606.07155v1 Announce Type: new Abstract: Shallow water equations (SWE) are fundamental models in fluid dynamics that are essential for studying a wide range of geophysical and engineering phenomena. In many practical applications, uncertainties arising from initial conditions and bottom topography must be taken into account, motivating the development of stable and accurate numerical methods for stochastic SWE. Building on the hyperbolicity-preserving stochastic Galerkin formulation...
Unified Regularization of 2D Singular Integrals for Axisymmetric Galerkin BEM in Eddy-Current Evaluation
arXiv:2601.19542v2 Announce Type: replace Abstract: This paper presents an axisymmetric Galerkin boundary element method (BEM) for modeling eddy-current interactions between excitation coils and conductive objects. The formulation derives boundary integral equations from the Stratton-Chu representation for the azimuthal component of the vector potential in both air and conductive regions. The central contribution is a unified regularization framework for the two-dimensional (2D) singular...
Unified Regularization of 2D Singular Integrals for Axisymmetric Galerkin BEM in Eddy-Current Evaluation
arXiv:2601.19542v2 Announce Type: replace-cross Abstract: This paper presents an axisymmetric Galerkin boundary element method (BEM) for modeling eddy-current interactions between excitation coils and conductive objects. The formulation derives boundary integral equations from the Stratton-Chu representation for the azimuthal component of the vector potential in both air and conductive regions. The central contribution is a unified regularization framework for the two-dimensional (2D)...
Optimal error estimates for a discontinuous Galerkin method on curved boundaries with polygonal meshes
Announce Type: replace Abstract: We consider a discontinuous Galerkin method for the numerical solution of boundary value problems in two-dimensional domains with curved boundaries. A key challenge in this setting is the potential loss of convergence order due to approximating the physical domain by a polygonal mesh. Unless boundary conditions can be accurately transferred from the true boundary to the computational one, such geometric approximation errors generally lead to suboptimal...
Pressure-robust and quasioptimal Discontinuous Galerkin discretisations of the $p$-Stokes problem
arXiv:2606.09586v1 Announce Type: new Abstract: In the present paper, we propose Local Discontinuous Galerkin (LDG) approximations for a nonlinear system of $p$-Stokes type, having $(p,\delta)$-structure. On the basis of the primal formulation, we prove well-posedness and stability (a priori estimates) of the methods under truly minimal regularity assumptions. We show that the first method possesses a pressure-robust and quasi-optimal error estimate, and discuss its consequences.
Numerical analysis of the second-order time-dependent saddle point Maxwell system via a parameter-free discontinuous Galerkin method: The first optimal ${\bf L}^{2}$-norm error estimates
Announce Type: new Abstract: We present a novel parameter-free discontinuous Galerkin (dG) finite element method (FEM) for the time-dependent Maxwell system formulated as a saddle point problem. We establish the stability of the proposed semi-discrete problem and derive optimal error estimates in energy and \( {\bf L}^{2} \) norms for the electric field variable, as well as in \( L^{2} \) norm for the potential function. To the best of our knowledge, this work provides the first optimal \(...
The Immersed Discontinuous Galerkin Method for Elliptic Interface Problems
arXiv:2606.01814v1 Announce Type: new Abstract: This paper is devoted to construction and convergence analysis of the linear explicit immersed finite element (IFE) function. For the interface elements, the proposed IFE functions precisely satisfy the interface conditions on the actual interface. The IFE functions are constructed in an explicit form and can be obtained directly without solving any auxiliary problems or local linear systems.
Neural Galerkin Normalizing Flows for Bayesian Inference of Diffusions with Inaccessible Boundaries
Announce Type: new Abstract: One of the primary challenges in Bayesian inference on the parameters of a diffusion model from discrete observations is the unavailability of an analytical expression for the transition density function between consecutive observation times, which is needed to derive the likelihood function. Extending previous studies that solve Fokker-Planck (FP) type partial differential equations with Normalizing Flows, we propose a new Normalizing Flow architecture to learn...
Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods
arXiv:2508.21427v2 Announce Type: replace Abstract: The ultra--relativistic Euler equations describe gases in the relativistic case when the thermal energy dominates. These equations for an ideal gas are given in terms of the pressure, the spatial part of the dimensionless four-velocity, and the particle density. Kunik et al.\ (2024, https://doi.org/10.1016/j.jcp.2024.113330) proposed genuine multi--dimensional benchmark problems for the ultra--relativistic Euler equations.