Applied Numerical Mathematics最新文献_第2页

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

2D and 3D reconstructions in acousto-electric tomography via two-point gradient Kaczmarz-type algorithm 基于两点梯度kaczmarz型算法的声电层析成像二维和三维重建

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-08-11 DOI: 10.1016/j.apnum.2025.07.015

Kai Zhu, Min Zhong

{"title":"2D and 3D reconstructions in acousto-electric tomography via two-point gradient Kaczmarz-type algorithm","authors":"Kai Zhu, Min Zhong","doi":"10.1016/j.apnum.2025.07.015","DOIUrl":"10.1016/j.apnum.2025.07.015","url":null,"abstract":"<div><div>This paper presents a Kaczmarz type two-point gradient algorithm with the general convex penalty functional <span><math><mstyle><mi>Θ</mi></mstyle></math></span> (KTPG-<span><math><mstyle><mi>Θ</mi></mstyle></math></span>), for efficient reconstruction of conductivity in acousto-electric tomography (AET). The algorithm optimizes a convex functional with flexible non-smooth regularization terms, such as <span><math><msup><mi>L</mi><mn>1</mn></msup></math></span>-like and total variation-like, to handle sparse and discontinuous conductivity distributions. By cyclically processing the measurement equations and incorporating an acceleration strategy, the proposed method achieves high computational efficiency while ensuring convergence. Numerical experiments on both synthetic and realistic phantoms demonstrate the method’s superior accuracy, strong noise robustness, and ability to resolve fine details. Beyond AET, the KTPG-<span><math><mstyle><mi>Θ</mi></mstyle></math></span> framework can be applied to a wide range of nonlinear inverse problems involving systems of equations, showcasing its potential for broader applications in science and engineering.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"218 ","pages":"Pages 220-237"},"PeriodicalIF":2.4,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886790","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

Semi-implicit fully exactly well-balanced schemes for the two-layer shallow water system 双层浅水系统的半隐式完全精确平衡方案

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-29 DOI: 10.1016/j.apnum.2025.07.014

C. Caballero-Cárdenas , M.J. Castro , C. Chalons , T. Morales de Luna , M.L. Muñoz-Ruiz

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

Space-time parallel solvers for reaction-diffusion problems forming Turing patterns 形成图灵模式的反应扩散问题的时空并行求解器

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-23 DOI: 10.1016/j.apnum.2025.07.012

Andrés Arrarás , Francisco J. Gaspar , Iñigo Jimenez-Ciga , Laura Portero

{"title":"Space-time parallel solvers for reaction-diffusion problems forming Turing patterns","authors":"Andrés Arrarás , Francisco J. Gaspar , Iñigo Jimenez-Ciga , Laura Portero","doi":"10.1016/j.apnum.2025.07.012","DOIUrl":"10.1016/j.apnum.2025.07.012","url":null,"abstract":"<div><div>In recent years, parallelization has become a strong tool to avoid the limits of classical sequential computing. In the present paper, we introduce four space-time parallel methods that combine the parareal algorithm with suitable splitting techniques for the numerical solution of reaction-diffusion problems. In particular, we consider a suitable partition of the elliptic operator that enables the parallelization in space by using splitting time integrators. Those schemes are then chosen as the propagators of the parareal algorithm, a well-known parallel-in-time method. Both first- and second-order time integrators are considered for this task. The resulting space-time parallel methods are applied to integrate reaction-diffusion problems that model Turing pattern formation. This phenomenon appears in chemical reactions due to diffusion-driven instabilities, and rules the pattern formation for animal coat markings. Such reaction-diffusion problems require fine space and time meshes for their numerical integration, so we illustrate the usefulness of the proposed methods by solving several models of practical interest.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"218 ","pages":"Pages 91-108"},"PeriodicalIF":2.4,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144720946","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

Robust globally divergence-free weak Galerkin variational data assimilation method for convection-dominated Oseen equations 对流占优Oseen方程的鲁棒全局无发散弱Galerkin变分数据同化方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-22 DOI: 10.1016/j.apnum.2025.07.011

Xian Zhang, Ya Min, Minfu Feng

{"title":"Robust globally divergence-free weak Galerkin variational data assimilation method for convection-dominated Oseen equations","authors":"Xian Zhang, Ya Min, Minfu Feng","doi":"10.1016/j.apnum.2025.07.011","DOIUrl":"10.1016/j.apnum.2025.07.011","url":null,"abstract":"<div><div>This paper presents a weak Galerkin (WG) finite element method based on the variational approach for data assimilation of the unsteady convection-dominated Oseen equation. The WG scheme uses piecewise polynomials of degrees <em>k</em>(<span><math><mi>k</mi><mo>≥</mo><mn>1</mn></math></span>) and <span><math><mi>k</mi><mo>−</mo><mn>1</mn></math></span> respectively for the approximations of the velocity and the pressure in the interior of elements, and uses piecewise polynomials of degree <em>k</em> for their numerical traces on the interfaces of elements. The method is shown to yield globally divergence-free approximations of the velocity and initial value. It is proved that the velocity error in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm has a Reynolds-robust error bound with quasi-optimal convergence order <span><math><mi>k</mi><mo>+</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span> in the convection-dominated region. To solve the discrete optimality system efficiently, the conjugate gradient iterative algorithm is developed, which also preserves the globally divergence-free property of WG scheme. Numerical experiments are provided to verify the obtained theoretical results.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"218 ","pages":"Pages 22-42"},"PeriodicalIF":2.2,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686025","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

FEM approximation of dynamic contact problem for fracture under fluid volume control using generalized HHT-α and semi-smooth Newton methods 流体体积控制下裂缝动态接触问题的广义HHT-α和半光滑牛顿法有限元逼近

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-22 DOI: 10.1016/j.apnum.2025.07.009

Victor A. Kovtunenko , Yves Renard

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