Applied Numerical Mathematics最新文献_第2页

Discrete gradient methods for port-Hamiltonian differential-algebraic equations 波特-哈密顿微分代数方程的离散梯度方法

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2026-05-01 Epub Date: 2025-12-27 DOI: 10.1016/j.apnum.2025.12.006

Philipp L. Kinon , Riccardo Morandin , Philipp Schulze

引用次数: 0

Two-grid mixed finite element method with backward Euler fully discrete scheme for the nonlinear schrödinger equation 用反向欧拉完全离散格式的两网格混合有限元法求解非线性schrödinger方程

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2026-05-01 Epub Date: 2026-01-03 DOI: 10.1016/j.apnum.2025.12.009

Zhikun Tian , Jianyun Wang , Jie Zhou

引用次数: 0

Finite element simulation of modified Poisson-Nernst-Planck/Navier-Stokes model for compressible electrolytes under mechanical equilibrium 力学平衡下可压缩电解质修正Poisson-Nernst-Planck/Navier-Stokes模型的有限元模拟

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2026-05-01 Epub Date: 2026-01-23 DOI: 10.1016/j.apnum.2026.01.011

Ankur Ankur , Ram Jiwari , Satyvir Singh

{"title":"Finite element simulation of modified Poisson-Nernst-Planck/Navier-Stokes model for compressible electrolytes under mechanical equilibrium","authors":"Ankur Ankur , Ram Jiwari , Satyvir Singh","doi":"10.1016/j.apnum.2026.01.011","DOIUrl":"10.1016/j.apnum.2026.01.011","url":null,"abstract":"<div><div>This work presents a finite element method for a modified Poisson–Nernst–Planck/Navier–Stokes (PNP/NS) model under the mechanical equilibrium, developed for compressible electrolytes. The modification is based on the new model proposed by Dreyer, Guhlke and M<span><math><mover><mi>u</mi><mo>¨</mo></mover></math></span>ller [1], where the diffusion flux in the classical PNP system is replaced with an implicitly involved new diffusion flux, leading to fractional nonlinearity. He and Sun [2] previously developed a numerical approach for another type of modification, where the Poisson equation in the PNP system was substituted with a fourth-order elliptic equation. Another key contribution of this work is the reduction of the equilibrium system to a modified Poisson–Boltzmann system. The proposed numerical scheme is capable of handling both compressible and incompressible regimes by employing a bulk modulus parameter, which governs the fluid’s compressibility and enables seamless transition between these regimes. To emphasize practical relevance, we discuss the implications of compressible electrolytes in the context of double-layer capacitance behavior. We also conduct numerical simulations over various domains to demonstrate its applicability under various operating conditions, including temperature fluctuations and variations in the bulk modulus. The numerical results validate the accuracy and robustness of our computational scheme and demonstrate that the observed limiting behavior for the incompressible regime aligns with the theoretical trends anticipated by Dreyer et al. <span><span>[1]</span></span>.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"223 ","pages":"Pages 255-278"},"PeriodicalIF":2.4,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147384758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Efficient, accurate, and robust penalty-projection algorithm for parameterized stochastic Navier-Stokes flow problems 参数化随机Navier-Stokes流问题的有效、准确、鲁棒的惩罚-投影算法

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2026-05-01 Epub Date: 2026-01-21 DOI: 10.1016/j.apnum.2026.01.010

Neethu Suma Raveendran , Md. Abdul Aziz , Sivaguru S. Ravindran , Muhammad Mohebujjaman

{"title":"Efficient, accurate, and robust penalty-projection algorithm for parameterized stochastic Navier-Stokes flow problems","authors":"Neethu Suma Raveendran , Md. Abdul Aziz , Sivaguru S. Ravindran , Muhammad Mohebujjaman","doi":"10.1016/j.apnum.2026.01.010","DOIUrl":"10.1016/j.apnum.2026.01.010","url":null,"abstract":"<div><div>This paper presents and analyzes a fast, robust, efficient, and optimally accurate fully discrete splitting algorithm for the Uncertainty Quantification (UQ) of convection-dominated flow problems modeled by parameterized Stochastic Navier-Stokes Equations (SNSEs). The time-stepping algorithm is an implicit backward-Euler linearized method, grad-div and Ensemble Eddy Viscosity (EEV) regularized, and split using discrete Hodge decomposition. Moreover, the scheme’s sub-problems are all designed to have different Right-Hand-Side (RHS) vectors but the same system matrix for all realizations at each time-step. The stability of the algorithm is rigorously proven, and it has been shown that appropriately large grad-div stabilization parameters cause the splitting error to vanish. The proposed UQ algorithm is then combined with the Stochastic Collocation Methods (SCMs). Several numerical experiments are presented to verify the predicted convergence rates and performance of this superior scheme on benchmark problems with high expected Reynolds numbers (<em>Re</em>).</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"223 ","pages":"Pages 235-254"},"PeriodicalIF":2.4,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147384759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A stable multistep scheme for the transient Wigner equation: Efficient handling of scattering 瞬态Wigner方程的稳定多步格式：散射的有效处理

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2026-05-01 Epub Date: 2026-01-18 DOI: 10.1016/j.apnum.2026.01.009

Yidan Wang , Haiyan Jiang , Tiao Lu , Wenqi Yao

引用次数: 0

Derivative-free convergence analysis for Steffensen-type schemes for nonlinear equations 非线性方程steffensen型格式的无导数收敛分析

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2026-05-01 Epub Date: 2026-01-09 DOI: 10.1016/j.apnum.2026.01.003

Santhosh George , Muniyasamy M , Laurence Grammont

{"title":"Derivative-free convergence analysis for Steffensen-type schemes for nonlinear equations","authors":"Santhosh George , Muniyasamy M , Laurence Grammont","doi":"10.1016/j.apnum.2026.01.003","DOIUrl":"10.1016/j.apnum.2026.01.003","url":null,"abstract":"<div><div>Steffensen schemes have been constructed to approximate the solution of an operator equation, with the goal of avoiding the use of its derivatives. It is the reason why these schemes involve the first order divided difference operator. Until now, results on convergence order have been provided using Taylor series expansion, which implies that the operator must be several times differentiable. To be consistent with the nature of the Steffensen schemes, we propose a proof of the convergence order under assumptions that involve only the first and second order divided difference operators. In addition, the convergence order analysis for these Steffensen schemes is done here for the general case of Banach spaces, while it has been done only for finite-dimensional spaces so far. Until now, the assumptions required for semi-local analysis and those required for local analysis have been of a very different nature. A new idea was to unify these hypotheses; hence, we give a single set of convergence conditions. Moreover, our local convergence analysis provides consistently explicit convergence balls that are computable.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"223 ","pages":"Pages 101-120"},"PeriodicalIF":2.4,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145975293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A separate preconditioned primal-dual splitting algorithm for composite monotone inclusion problems 复合单调包含问题的单独预条件原对偶分裂算法

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2026-04-01 Epub Date: 2025-12-27 DOI: 10.1016/j.apnum.2025.12.004

Xiaokai Chang , Xingran Zhao , Long Xu

引用次数: 0

Error analysis on the mixed finite element method for a quad-curl problem with low-order terms in three dimensions 三维低阶项四旋度问题的混合有限元法误差分析

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2026-04-01 Epub Date: 2025-12-02 DOI: 10.1016/j.apnum.2025.11.011

Jikun Zhao , Kangcheng Deng , Chao Wang , Bei Zhang

{"title":"Error analysis on the mixed finite element method for a quad-curl problem with low-order terms in three dimensions","authors":"Jikun Zhao , Kangcheng Deng , Chao Wang , Bei Zhang","doi":"10.1016/j.apnum.2025.11.011","DOIUrl":"10.1016/j.apnum.2025.11.011","url":null,"abstract":"<div><div>This paper aims to develop a mixed finite element method for the three-dimensional quad-curl problem with low-order terms. We prove the regularity estimates on the solution to the primal weak problem under the assumption that the domain is a convex polyhedron. Subsequently, we introduce an auxiliary variable to reformulate the original problem as a mixed problem that consists of two curl-curl equations. Based on the regularity estimates, we establish the equivalence between the primal and mixed formulations. In this mixed finite element method, the primal and auxiliary variables are discretized by the Nédélec’s edge elements. We first derive the suboptimal error estimates for the mixed finite element method. In order to prove the optimal convergence, we construct a special projection with some good properties by using the Maxwell equation under the natural boundary condition. Then, by the duality argument, we prove the optimal error estimates for the approximation to the primal solution in the quad-curl equation. The numerical results illustrate the viability and optimal convergence of this method.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"222 ","pages":"Pages 17-31"},"PeriodicalIF":2.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145735273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Linear minimum-variance approximants for noisy data 噪声数据的线性最小方差近似

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2026-04-01 Epub Date: 2025-12-09 DOI: 10.1016/j.apnum.2025.12.002

Sergio López-Ureña, Dionisio F. Yáñez

引用次数: 0

High-order orthogonal spline collocation schemes for two-dimensional nonlinear problems 二维非线性问题的高阶正交样条配置格式

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2026-04-01 Epub Date: 2025-12-06 DOI: 10.1016/j.apnum.2025.12.001

Meirong Cheng, Qimin Li, Leijie Qiao

引用次数: 0