Applied Numerical Mathematics最新文献_第2页

A biharmonic solver based on Fourier extension with oversampling technique for arbitrary domain 基于傅里叶扩展和过采样技术的任意域双调和求解器

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-08-16 DOI: 10.1016/j.apnum.2025.08.005

Wenbin Li, Tinggang Zhao, Zhenyu Zhao

引用次数: 0

Fractional convection-diffusion systems in complex 2D and 3D geometries: A Bernoulli polynomial-based kernel method 复杂二维和三维几何中的分数对流扩散系统：基于伯努利多项式的核方法

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-08-15 DOI: 10.1016/j.apnum.2025.08.004

Mojtaba Fardi , Mahmoud A. Zaky , Babak Azarnavid

{"title":"Fractional convection-diffusion systems in complex 2D and 3D geometries: A Bernoulli polynomial-based kernel method","authors":"Mojtaba Fardi , Mahmoud A. Zaky , Babak Azarnavid","doi":"10.1016/j.apnum.2025.08.004","DOIUrl":"10.1016/j.apnum.2025.08.004","url":null,"abstract":"<div><div>This study presents an accurate meshless method for the efficient solution of nonlinear time-fractional convection-diffusion systems in complex two- and three-dimensional geometries. The proposed approach combines spatial discretization using a Bernoulli polynomial kernel function with temporal discretization via the backward differentiation formula. By employing positive definite kernels, the method achieves high spatial accuracy, while the use of the backward differentiation formula ensures high-order temporal accuracy. Convergence conditions and error bounds are rigorously analyzed using the Mittag-Leffler function. Error estimates are derived based on the spectral properties of the associated matrices, and inequalities describing error propagation over time are established. The method is tested on a variety of benchmark problems, including the Brusselator model and nonlinear coupled convection-diffusion systems, across both 2D and 3D domains. Extensive numerical experiments are carried out on various geometries-such as rectangular, circular, and spherical shapes-demonstrating the method’s robustness and accuracy in handling both regular and irregular computational domains.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"218 ","pages":"Pages 275-297"},"PeriodicalIF":2.4,"publicationDate":"2025-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896067","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

Adaptive SIPG method for approximations of parabolic boundary control problems with bilateral box constraints on Neumann boundary Neumann边界上双侧框约束抛物型边界控制问题逼近的自适应SIPG方法

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-08-13 DOI: 10.1016/j.apnum.2025.08.002

Ram Manohar , B․ V․ Rathish Kumar , Kedarnath Buda , Rajen Kumar Sinha

{"title":"Adaptive SIPG method for approximations of parabolic boundary control problems with bilateral box constraints on Neumann boundary","authors":"Ram Manohar , B․ V․ Rathish Kumar , Kedarnath Buda , Rajen Kumar Sinha","doi":"10.1016/j.apnum.2025.08.002","DOIUrl":"10.1016/j.apnum.2025.08.002","url":null,"abstract":"<div><div>This study presents an a posteriori error analysis of adaptive finite element approximations of parabolic boundary control problems with bilateral box constraints that act on a Neumann boundary. The control problem is discretized using the symmetric interior penalty Galerkin (SIPG) technique. We derive both reliable and efficient type residual-based error estimators coupling with the data oscillations. The implementation of these error estimators serves as a guide for the adaptive mesh refinement process, indicating whether or not more refinement is required. Although the control error estimator accurately captured control approximation errors, it had limitations in terms of guiding refinement localization in critical circumstances. To overcome this, an alternative control indicator was used in numerical tests. The results demonstrated the clear superiority of adaptive refinements over uniform refinements, confirming the proposed approach’s effectiveness in achieving accurate solutions while optimizing computational efficiency. Numerical experiments showcase the effectiveness of the derived error estimators.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"219 ","pages":"Pages 170-201"},"PeriodicalIF":2.4,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106357","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 posteriori error estimates for the finite element approximation of the convection–diffusion–reaction equation based on the variational multiscale concept 基于变分多尺度概念的对流扩散反应方程有限元近似的后验误差估计

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-08-11 DOI: 10.1016/j.apnum.2025.08.003

Ramon Codina , Hauke Gravenkamp , Sheraz Ahmed Khan

{"title":"A posteriori error estimates for the finite element approximation of the convection–diffusion–reaction equation based on the variational multiscale concept","authors":"Ramon Codina , Hauke Gravenkamp , Sheraz Ahmed Khan","doi":"10.1016/j.apnum.2025.08.003","DOIUrl":"10.1016/j.apnum.2025.08.003","url":null,"abstract":"<div><div>In this study, we employ the variational multiscale (VMS) concept to develop a posteriori error estimates for the stationary convection-diffusion-reaction equation. The variational multiscale method is based on splitting the continuous part of the problem into a resolved scale (coarse scale) and an unresolved scale (fine scale). The unresolved scale (also known as the sub-grid scale) is modeled by choosing it proportional to the component of the residual orthogonal to the finite element space, leading to the orthogonal sub-grid scale (OSGS) method. The idea is then to use the modeled sub-grid scale as an error estimator, considering its contribution in the element interiors and on the edges. We present the results of the a priori analysis and two different strategies for the a posteriori error analysis for the OSGS method. Our proposal is to use a scaled norm of the sub-grid scales as an a posteriori error estimate in the so-called stabilized norm of the problem. This norm has control over the convective term, which is necessary for convection-dominated problems. Numerical examples show the reliable performance of the proposed error estimator compared to other error estimators belonging to the variational multiscale family.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"218 ","pages":"Pages 238-260"},"PeriodicalIF":2.4,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886791","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 boundary-corrected weak Galerkin mixed finite method for elliptic interface problems with curved interfaces 具有弯曲界面的椭圆界面问题的边界修正弱Galerkin混合有限方法

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-08-06 DOI: 10.1016/j.apnum.2025.08.001

Yongli Hou , Yi Liu , Yanqiu Wang

引用次数: 0

A fast Fourier-Galerkin method for solving boundary integral equations on non-axisymmetric toroidal surfaces 求解非轴对称环面边界积分方程的快速傅立叶-伽辽金方法

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-24 DOI: 10.1016/j.apnum.2025.07.013

Yiying Fang , Ying Jiang , Jiafeng Su

{"title":"A fast Fourier-Galerkin method for solving boundary integral equations on non-axisymmetric toroidal surfaces","authors":"Yiying Fang , Ying Jiang , Jiafeng Su","doi":"10.1016/j.apnum.2025.07.013","DOIUrl":"10.1016/j.apnum.2025.07.013","url":null,"abstract":"<div><div>We propose a fast Fourier–Galerkin method for solving boundary integral equations (BIEs) on smooth, non-axisymmetric toroidal surfaces. Our approach begins by analyzing the structure of the integral kernel, revealing an exponential decay pattern in the Fourier coefficients after a shear transformation. Leveraging this decay, we design a truncation strategy that compresses the dense representation matrix into a sparse form with only <span><math><mi>O</mi><mo>(</mo><mi>N</mi><msup><mrow><mi>ln</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⁡</mo><mi>N</mi><mo>)</mo></math></span> nonzero entries, where <em>N</em> denotes the degrees of freedom. We rigorously prove that the truncated system retains the stability of the original Fourier–Galerkin formulation and achieves a quasi-optimal convergence rate of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mi>p</mi><mo>/</mo><mn>2</mn></mrow></msup><mi>ln</mi><mo>⁡</mo><mi>N</mi><mo>)</mo></math></span>, with <em>p</em> denoting the regularity of the exact solution. Numerical experiments corroborate our theoretical results, demonstrating both high accuracy and computational efficiency. Furthermore, we extend the proposed strategy to BIEs defined on surfaces diffeomorphic to the sphere, confirming the sparsity structure remains exploitable under broader geometric settings.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"218 ","pages":"Pages 73-90"},"PeriodicalIF":2.4,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144720943","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

Weak Galerkin spectral element methods for elliptic eigenvalue problems: Lower bound approximation and superconvergence 椭圆型特征值问题的弱Galerkin谱元方法：下界逼近和超收敛

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-22 DOI: 10.1016/j.apnum.2025.07.010

Jiajia Pan , Huiyuan Li

{"title":"Weak Galerkin spectral element methods for elliptic eigenvalue problems: Lower bound approximation and superconvergence","authors":"Jiajia Pan , Huiyuan Li","doi":"10.1016/j.apnum.2025.07.010","DOIUrl":"10.1016/j.apnum.2025.07.010","url":null,"abstract":"<div><div>Lower bound approximation and super-convergence of the weak Galerkin spectral element method for second-order elliptic eigenvalue problems are comprehensively investigated in this paper. At first, we establish the approximation spaces with diverse polynomial degrees of weak functions and weak gradients by using the one-to-one mapping from the reference element to each physical element. General weak Galerkin triangular/quadrilateral spectral element approximation schemes are then proposed for the eigenvalue problem of the second-order elliptic operators. A study on the well-posedness of our schemes is carried out, resulting in the constraint conditions on the polynomial degrees of the discrete weak function space and the discrete weak gradient space. Further, qualitative numerical analysis and numerical investigation are performed on a series of polynomial degree configurations for the weak function space and the weak gradient space. We obtain in the sequel the super-convergence of the numerical eigenvalues with the weak Galerkin spectral element methods for the first time, and discover some lower bound approximation scenario that has never been reported before in literature.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"218 ","pages":"Pages 182-200"},"PeriodicalIF":2.4,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144831172","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

H(div)-conforming IPDG FEM with pointwise divergence-free velocity field for the micropolar Navier-Stokes equations 微极Navier-Stokes方程的H（div）型无点发散速度场IPDG有限元

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-18 DOI: 10.1016/j.apnum.2025.07.007

Xinran Huang, Haiyan Su, Xinlong Feng

引用次数: 0

A novel amplifying methodology in Gauss-Legendre IRK integrations to cope with high-frequency stiff problems 高斯-勒让德IRK积分中处理高频刚性问题的一种新的放大方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-17 DOI: 10.1016/j.apnum.2025.07.006

Sanaz Hami Hassan Kiyadeh , Hosein Saadat , Ramin Goudarzi Karim , Ali Safaie , Fayyaz Khodadosti

{"title":"A novel amplifying methodology in Gauss-Legendre IRK integrations to cope with high-frequency stiff problems","authors":"Sanaz Hami Hassan Kiyadeh , Hosein Saadat , Ramin Goudarzi Karim , Ali Safaie , Fayyaz Khodadosti","doi":"10.1016/j.apnum.2025.07.006","DOIUrl":"10.1016/j.apnum.2025.07.006","url":null,"abstract":"<div><div>This work presents a new amplification methodology based on the widely used Gauss-Legendre implicit Runge-Kutta integrations by addressing the phase lag and amplification factor. The novel methodology focuses on these two elements, which are the complex amplifiers associated with the GLIRK integrations.</div><div>To enhance the amplifier capabilities of the GLIRK integrations, we introduce two novel equations that clarify the relationships between the amplification factor and phase lag. This paper culminates in the improvement of two well-defined GLIRK integrations, each carefully designed to eliminate both the phase lag and the amplification factor in practical applications. The examination of absolute stability regions in the complex plane, as well as stability regions in the <em>z</em>-<em>v</em> plane, is relevant to the new GLIRK integrations presented.</div><div>To satisfy the admissibility of the new methodology, we establish a competitive environment alongside the classical GLIRK integration.</div><div>This competitive space includes numerical examples that demonstrate the low cost of the new amplified GLIRK integrations in addressing stiff problems with high frequency. Ultimately, this cost-effectiveness and superiority become increasingly evident as the frequency of the stiff problems increases.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"218 ","pages":"Pages 43-57"},"PeriodicalIF":2.2,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144694462","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 third-order finite difference weighted essentially non-oscillatory scheme with shallow neural network 具有浅层神经网络的三阶有限差分加权本质非振荡格式

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-14 DOI: 10.1016/j.apnum.2025.07.005

Kwanghyuk Park , Xinjuan Chen , Dongjin Lee , Jiaxi Gu , Jae-Hun Jung

引用次数: 0