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A second-order face-centred finite volume method (FCFV) is proposed. Contrary to the more popular cell-centred and vertex-centred finite volume (FV) techniques, the proposed method defines the solution on the faces of the mesh (edges in two…

Numerical Analysis · Mathematics 2019-11-12 Luan M Vieira , Matteo Giacomini , Ruben Sevilla , Antonio Huerta

The Finitely Extensible Nonlinear Elastic (FENE) dumbbell model is a widely used mathematical model for complex fluids. Direct simulation of the FENE Fokker--Planck equation is computationally challenging due to high dimensionality and…

Numerical Analysis · Mathematics 2026-02-10 Runkai Feng , Jie Shen , Haijun Yu

This work introduces a new higher-order accurate super compact (HOSC) finite difference scheme for solving complex unsteady three-dimensional (3D) non-Newtonian fluid flow problems. As per the author's knowledge, the proposed scheme is the…

Fluid Dynamics · Physics 2024-07-30 Ashwani Punia , Rajendra K. Ray

In this paper, we propose an efficient quadratic interpolation formula utilizing solution gradients computed and stored at nodes and demonstrate its application to a third-order cell-centered finite-volume discretization on tetrahedral…

Numerical Analysis · Mathematics 2023-07-07 Hiroaki Nishikawa , Jeffery A. White

We develop arbitrarily high-order, stationarity-preserving stabilized finite element methods for multidimensional nonlinear hyperbolic balance laws on Cartesian grids. We aim at approximating all the steady states of the problem at hand,…

Numerical Analysis · Mathematics 2026-03-25 Moussa Ziggaf , Davide Torlo , Mario Ricchiuto

We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier-Stokes equations with a free surface for the accurate simulation of nonlinear and dispersive water waves in the time domain. The…

Numerical Analysis · Mathematics 2024-06-06 Anders Melander , Max E. Bitsch , Dong Chen , Allan P. Engsig-Karup

We develop a fast and accurate method for 3D alignment, recovering the rotation and translation that best align a reference volume with a noisy observation. Classical matched filtering evaluates cross-correlation over a large discretized…

Signal Processing · Electrical Eng. & Systems 2026-03-17 Fabian Kruse , Valentin Debarnot , Vinith Kishore , Ivan Dokmanić

This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Non-oscillatory…

Numerical Analysis · Mathematics 2024-01-31 Ian C. T. May , Dongwook Lee

Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation for…

Numerical Analysis · Mathematics 2025-06-13 Daniel A. Serino , Qi Tang , Xian-Zhu Tang , Tzanio V. Kolev , Konstantin Lipnikov

Shallow water moment equations are reduced-order models for free-surface flows that allow to represent vertical variations of the velocity profile at the expense of additional evolution equations for a number of additional variables, so…

Numerical Analysis · Mathematics 2025-07-02 Mirco Ciallella , Julian Koellermeier

We present a detailed QCD analysis of nucleon structure functions $xF_3 (x, Q^2)$, based on Laplace transforms and Jacobi polynomials approach. The analysis corresponds to the next-to-leading order and next-to-next-to-leading order…

High Energy Physics - Phenomenology · Physics 2016-10-05 S. Mohammad Moosavi Nejad , Hamzeh Khanpour , S. Atashbar Tehrani , Mahdi Mahdavi

Superlinear convergence has been an elusive goal for black-box nonsmooth optimization. Even in the convex case, the subgradient method is very slow, and while some cutting plane algorithms, including traditional bundle methods, are popular…

Optimization and Control · Mathematics 2019-07-30 Adrian Lewis , Calvin Wylie

Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…

Numerical Analysis · Mathematics 2024-07-15 Meng Li , Yihang Guo , Jingjiang Bi

A cell-centered implicit-explicit updated Lagrangian finite volume scheme on unstructured grids is proposed for a unified first order hyperbolic formulation of continuum fluid and solid mechanics. The scheme provably respects the stiff…

Numerical Analysis · Mathematics 2022-01-26 Walter Boscheri , Simone Chiocchetti , Ilya Peshkov

The random feature method (RFM), a mesh-free machine learning-based framework, has emerged as a promising alternative for solving PDEs on complex domains. However, for large three-dimensional nonlinear problems, attaining high accuracy…

Numerical Analysis · Mathematics 2025-10-07 Longze Tan

The paper considers the numerical solution of nonlinear integral equations using the Newton-Kantorovich method with the mpmath library. High-precision quadrature of the kernel K(t, s, u) with respect to the variable s for fixed t increases…

Numerical Analysis · Mathematics 2025-11-03 Kirill A. Chertoganov , Valery I. Shipalov

We propose a new approach to the numerical solution of ergodic problems arising in the homogenization of Hamilton-Jacobi (HJ) equations. It is based on a Newton-like method for solving inconsistent systems of nonlinear equations, coming…

Numerical Analysis · Mathematics 2016-02-11 Simone Cacace , Fabio Camilli

In this paper, we introduce second order and fourth order space discretization via finite difference implementation of the finite element method for solving Fokker-Planck equations associated with irreversible processes. The proposed…

Numerical Analysis · Mathematics 2023-10-12 Chen Liu , Yuan Gao , Xiangxiong Zhang

In recent years, interface quasi-Newton methods have gained growing attention in the fluid-structure interaction community by significantly improving partitioned solution schemes: They not only help to control the inherent added-mass…

Computational Engineering, Finance, and Science · Computer Science 2020-01-23 Thomas Spenke , Norbert Hosters , Marek Behr

We develop a monotone finite volume method for the time fractional Fokker-Planck equations and theoretically prove its unconditional stability. We show that the convergence rate of this method is order 1 in space and if the space grid…

Numerical Analysis · Mathematics 2017-11-03 Yingjun Jiang , Xuejun Xu