Computers & Mathematics with Applications最新文献_第7页

Accelerating the Lax-Wendroff time discretization method for the first-order acoustic wave equation simulation by designing proper SGFD schemes 通过设计合适的SGFD格式，加速一阶声波方程模拟的Lax-Wendroff时间离散化方法

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-03-01 Epub Date: 2026-01-02 DOI: 10.1016/j.camwa.2025.12.025

Wenquan Liang , Yanfei Wang

引用次数: 0

Analysis of the weighted shifted boundary method for the Poisson and Stokes problems 泊松和斯托克斯问题的加权移边法分析

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-03-01 Epub Date: 2025-12-27 DOI: 10.1016/j.camwa.2025.12.011

Nabil M. Atallah , Claudio Canuto , Guglielmo Scovazzi

{"title":"Analysis of the weighted shifted boundary method for the Poisson and Stokes problems","authors":"Nabil M. Atallah , Claudio Canuto , Guglielmo Scovazzi","doi":"10.1016/j.camwa.2025.12.011","DOIUrl":"10.1016/j.camwa.2025.12.011","url":null,"abstract":"<div><div>The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by properly <em>shifting</em> the <em>location</em> and <em>values</em> of the boundary conditions. This avoids integration over cut cells and the associated implementation issues. Recently, the Weighted SBM (WSBM) was proposed for the Navier-Stokes equations with free surfaces and the Stokes flow with moving boundaries. The attribute “weighted” in the name WSBM stems from the fact that its variational form is weighted with the elemental volume fraction of active fluid. The motivation for the development of the WSBM was the preservation of the volume of active fluid to a higher degree of accuracy, which in turn resulted in improved stability and robustness characteristics in moving-boundary, time-dependent simulations. In this article, we present the numerical analysis of the WSBM formulations for the Poisson and Stokes problems. We give mathematical conditions under which the bilinear forms defining the discrete variational formulations are uniformly coercive (Poisson problem) or inf-sup stable (Stokes problem). By these results, stability and optimal convergence is proven in the natural norm; <em>L</em><sup>2</sup>-error estimates can also be derived.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 63-85"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842522","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

Unconditionally convergent fourth-order compact difference methods for Quasi-linear convection-diffusion equations 拟线性对流扩散方程的无条件收敛四阶紧致差分方法

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-03-01 Epub Date: 2026-01-19 DOI: 10.1016/j.camwa.2026.01.018

Mengling Wu , Hongling Hu , Kejia Pan , Wei Wu

{"title":"Unconditionally convergent fourth-order compact difference methods for Quasi-linear convection-diffusion equations","authors":"Mengling Wu , Hongling Hu , Kejia Pan , Wei Wu","doi":"10.1016/j.camwa.2026.01.018","DOIUrl":"10.1016/j.camwa.2026.01.018","url":null,"abstract":"<div><div>In this paper, we propose an unconditionally convergent implicit compact difference method for the quasi-linear convective diffusion equation. First, we use Taylor expansion combined with the truncation error residual correction method to discretize the first-order derivative in the temporal direction, while the first- and second-order derivatives in the spatial direction are approximated by the consistent fourth-order boundary schemes and the fourth-order difference method, respectively. We develop a two-level scheme with <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mrow><msup><mi>τ</mi><mn>2</mn></msup><mo>+</mo><msup><mi>h</mi><mn>4</mn></msup></mrow><mo>)</mo></mrow></mrow></math></span>. Secondly, the convergence of the scheme in the <em>L</em><sup>∞</sup> norm has been proven. To further improve computational efficiency, we apply Richardson extrapolation to improve the temporal accuracy of the scheme to fourth-order, i.e., <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mrow><msup><mi>τ</mi><mn>4</mn></msup><mo>+</mo><msup><mi>h</mi><mn>4</mn></msup></mrow><mo>)</mo></mrow></mrow></math></span>. Finally, we present numerical examples to verify the theoretical analysis and the efficiency of our proposed method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 268-281"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146001484","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

Solving fluid flow problems in space-time with multiscale stabilization: Formulation and examples 用多尺度稳定方法求解时空流体流动问题：公式和实例

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-03-01 Epub Date: 2025-12-30 DOI: 10.1016/j.camwa.2025.12.019

Biswajit Khara , Robert Dyja , Kumar Saurabh , Anupam Sharma , Baskar Ganapathysubramanian

引用次数: 0

Low-cost adaptive characteristic finite element method for incompressible natural convection problems 不可压缩自然对流问题的低成本自适应特征有限元方法

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-03-01 Epub Date: 2025-12-26 DOI: 10.1016/j.camwa.2025.12.008

Bowen Ren , Jilian Wu , Ning Li , Leilei Wei

{"title":"Low-cost adaptive characteristic finite element method for incompressible natural convection problems","authors":"Bowen Ren , Jilian Wu , Ning Li , Leilei Wei","doi":"10.1016/j.camwa.2025.12.008","DOIUrl":"10.1016/j.camwa.2025.12.008","url":null,"abstract":"<div><div>This paper firstly adopt a novel low-complexity finite element method for incompressible natural convection problems, which is based on the characteristic finite element method (CFEM) and achieves higher-order accuracy by introducing the time filter (TF) technique. The new method effectively addresses inherent limitations of the characteristic finite element method while retaining its essential advantages. By applying the TF to postprocess solutions obtained from the first-order characteristic finite element method (CFEM-1), we achieve a non-intrusive enhancement to existing code frameworks, boosting temporal accuracy by one order. Secondly, this paper constructs two error operators without increasing complexity, thus facilitating the construction of a new adaptive algorithm conveniently. Additionally, we consturct adaptive CFEM and adaptive CFEM plus TF. Subsequently, this paper proves the unconditional stability of the constant time stepsize CFEM plus TF. Lastly, numerical experiments presented to validate the theoretical analysis and substantiate the aforementioned propositions.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 19-39"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842449","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

Numerical methods and analysis for magnetohydrodynamics slip flow and heat transfer of Jeffrey nanofluid with tempered fractional constitutive relationship 具有回火分数本构关系的Jeffrey纳米流体磁流体力学、滑移流动和传热的数值方法与分析

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-03-01 Epub Date: 2026-01-14 DOI: 10.1016/j.camwa.2025.12.030

Wenxin Zheng , Fawang Liu , Shujuan Lü , Ian Turner , Libo Feng

{"title":"Numerical methods and analysis for magnetohydrodynamics slip flow and heat transfer of Jeffrey nanofluid with tempered fractional constitutive relationship","authors":"Wenxin Zheng , Fawang Liu , Shujuan Lü , Ian Turner , Libo Feng","doi":"10.1016/j.camwa.2025.12.030","DOIUrl":"10.1016/j.camwa.2025.12.030","url":null,"abstract":"<div><div>In this work, the magnetohydrodynamic (MHD) flow and heat transfer for a Jeffrey nanofluid flowing over a semi-infinite plate subjected to slip effects is considered. Firstly, the standard constitutive equation of a Jeffrey fluid is generalized to incorporate the tempered fractional derivative to describe the nonlocal but finite relaxation process, which leads to a novel tempered momentum equation. Combined with a tempered energy equation, the coupled momentum and energy system of a Jeffrey nanofluid is formulated. Secondly, the Legendre spectral method is employed to the tempered fractional coupled model, in which the modified shifted Grünwald superconvergence formula is proposed to discretize the tempered fractional derivative. To enhance computational efficiency, a fast algorithm is further developed, for which the stability and convergence analysis are rigorously established. Finally, some numerical examples are performed to confirm the efficiency of the proposed numerical schemes and to investigate the impacts of important model parameters on the variations of fluid movement and thermal transfer.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 229-250"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978238","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

Error analysis of the first-order and second-order fully discrete schemes for the Caginalp model Caginalp模型一阶和二阶完全离散格式的误差分析

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-03-01 Epub Date: 2026-02-01 DOI: 10.1016/j.camwa.2026.01.028

Lixian Zhao, Yeping Li

引用次数: 0

Mathematical relationships and novel extensions of MLPG variants MLPG变体的数学关系和新扩展

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-03-01 Epub Date: 2026-01-10 DOI: 10.1016/j.camwa.2026.01.001

Elham Gholamipour , Ahmad Shirzadi , Hossein Hosseinzadeh , Vladimir Sladek , Jan Sladek

{"title":"Mathematical relationships and novel extensions of MLPG variants","authors":"Elham Gholamipour , Ahmad Shirzadi , Hossein Hosseinzadeh , Vladimir Sladek , Jan Sladek","doi":"10.1016/j.camwa.2026.01.001","DOIUrl":"10.1016/j.camwa.2026.01.001","url":null,"abstract":"<div><div>While various Meshless Local Petrov-Galerkin (MLPG) method variants exist, primarily distinguished by their choice of test functions in local subdomains, the mathematical relationships among these approaches remain unexplored. This paper establishes rigorous connections between existing MLPG formulations and proposes novel extensions based on an analysis of test function smoothness. It is shown that MLPG5, which employs Heaviside step test functions, corresponds to the mean value of MLPG2 (the collocation method), while MLPG4, using logarithmic test functions, is proven equivalent to the mean value of MLPG5 over the radius of local subdomains. Building on these insights, a systematic framework for generating new MLPG variants is introduced by leveraging the smoothness properties of test functions. All existing and newly proposed MLPG variants are demonstrated to have local weak forms equivalent to the original strong-form equations. This equivalence establishes the unique solvability of the methods, addressing long-standing questions regarding their consistency. Comprehensive numerical experiments validate the theoretical findings, confirming both the inter-variant relationships and the robustness of the newly extended MLPG variants.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 212-228"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927228","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

ITPINN : Integral-trainable physics informed neural network for solving high-dimensional evolution non-local partial differential equations 求解高维演化非局部偏微分方程的积分可训练物理通知神经网络

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-03-01 Epub Date: 2026-01-21 DOI: 10.1016/j.camwa.2026.01.019

Wenkai Liu , Fanhai Zeng , Hong Li , Yang Liu

{"title":"ITPINN : Integral-trainable physics informed neural network for solving high-dimensional evolution non-local partial differential equations","authors":"Wenkai Liu , Fanhai Zeng , Hong Li , Yang Liu","doi":"10.1016/j.camwa.2026.01.019","DOIUrl":"10.1016/j.camwa.2026.01.019","url":null,"abstract":"<div><div>In this paper, we develop a new physics informed neural network (PINN) method, named integral-trainable PINN (ITPINN), to solve high-dimensional non-local partial differential equations (PDEs), involving PDEs with fractional derivatives (Caputo derivative and Riemann-Liouville derivative) or multiple integral. In the ITPINN framework, we perform integration by parts on the original integral to obtain a new constraint condition, which forms a coupled system with the original equation. We consider the integral terms as unknown functions in the coupled system and construct a neural network with three output terms, one for predicting the exact solution, one for predicting the original integral term, and one for approximating the new integral obtained by integration by parts. The network is used as a surrogate model for fractional derivatives or multiple integral, which allows approximation of the fractional derivatives or multiple integral to be achieved by training the network. The proposed method omits the process of discretizing the integral term using traditional numerical methods, such as finite difference method or interpolation approximation. Moreover, the physical information obtained from integration by parts is used to construct a new supervised learning task to further constrain the surrogate model for the integral terms. Several experiments are used to illustrate the performance of the ITPINN. The numerical results confirm that our proposed method can effectively solve high-dimensional evolution non-local PDEs, such as 50D problems. Compared to fractional PINN (fPINN) and auxiliary PINN (A-PINN), the ITPINN can achieve higher prediction accuracy and save more training time. In particular, we also test the robustness of the ITPINN under interference with noise intensities ranging from 0.01% to 50% and further discuss its scalability in 100D and 1000D problems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 282-317"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014491","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 discrete perfectly matched layer for peridynamic scalar waves in two-dimensional viscous media 二维粘性介质中周动力标量波的离散完美匹配层

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-03-01 Epub Date: 2025-12-29 DOI: 10.1016/j.camwa.2025.12.007

Yu Du , Yonglin Li , Jiwei Zhang

引用次数: 0