Journal of Computational and Applied Mathematics最新文献

{"title":"An efficient scalar auxiliary variable (SAV) spectral Petrov–Galerkin approximation for nonlinear Hamiltonian systems","authors":"Jing An ,&nbsp;Waixiang Cao ,&nbsp;Zhimin Zhang","doi":"10.1016/j.cam.2025.117127","DOIUrl":"10.1016/j.cam.2025.117127","url":null,"abstract":"<div><div>In this paper, a new scalar auxiliary variable (SAV) spectral Petrov–Galerkin approximation is proposed and studied for nonlinear Hamiltonian systems. The new algorithm is built upon the SAV approach and the spectral Petrov–Galerkin (SPG) method, which enjoys both the advantages of SAV and SPG methods such as the properties of energy preserving and high order accuracy. A rigorous theoretical analysis is provided to show that the proposed algorithm is well-posed and convergent. Furthermore, the conservation properties are investigated. In particular, we prove that SAV-SPG method preserves the modified energy exactly and maintains the symplectic structure up to a spectral accuracy. Numerical experiments have been conducted to verify the efficacy of our algorithm.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117127"},"PeriodicalIF":2.6,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269739","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}

{"title":"Local projection stabilization methods for H(curl) and H(div) advection problems","authors":"Yangfan Luo ,&nbsp;Jindong Wang ,&nbsp;Shuonan Wu","doi":"10.1016/j.cam.2025.117129","DOIUrl":"10.1016/j.cam.2025.117129","url":null,"abstract":"<div><div>We devise local projection stabilization (LPS) methods for advection problems in the <span><math><mi>H</mi></math></span>(curl) and <span><math><mi>H</mi></math></span>(div) spaces, employing conforming finite element spaces of arbitrary order within a unified framework. The key ingredient is a local inf–sup condition, enabled by enriching the approximation space with appropriate <span><math><mi>H</mi></math></span>(d) bubble functions (with d <span><math><mo>=</mo></math></span> curl or div). This enrichment allows for the construction of a modified interpolation operator, which is crucial for establishing optimal <em>a priori</em> error estimates in the energy norm. Numerical examples are presented to verify both the theoretical results and the stabilization properties of the proposed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117129"},"PeriodicalIF":2.6,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269740","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}

{"title":"Advanced methods of boundary integral equations for Laplace’s equation: Relations to method of fundamental solutions","authors":"Li-Ping Zhang ,&nbsp;Zi-Cai Li ,&nbsp;Hung-Tsai Huang ,&nbsp;Ming-Gong Lee","doi":"10.1016/j.cam.2025.117135","DOIUrl":"10.1016/j.cam.2025.117135","url":null,"abstract":"<div><div>Consider Laplace’s equation in a bounded simply-connected domain <span><math><mi>S</mi></math></span>. The harmonic functions in <span><math><mi>S</mi></math></span> can be represented by boundary integral equations of the first kind (BIE), which is defined on the domain boundary <span><math><mrow><mi>Γ</mi><mspace></mspace><mrow><mo>(</mo><mo>=</mo><mi>∂</mi><mi>S</mi><mo>)</mo></mrow></mrow></math></span>. The unknowns are solved via the source nodes <span><math><mi>Q</mi></math></span> on <span><math><mi>Γ</mi></math></span>, and their discrete algorithms are called the conventional boundary integral equation method (BIEM). From the Sobolev extension theory, the harmonic solutions can be extended to a larger simply-connected domain <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span> with <span><math><mrow><mi>S</mi><mo>⊂</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>R</mi></mrow></msub></mrow></math></span>. We renovate the BIEM by moving the source nodes <span><math><mi>Q</mi></math></span> from <span><math><mi>Γ</mi></math></span> to <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span>, to eliminate the singularity of the BIEM. Their discrete algorithms are simple and straightforward, and called the discrete boundary integral equation method (DBIEM). The main effort of this paper is to explore the error analysis of the DBIEM via Galerkin approaches. An important application of the error analysis is for the method of fundamental solutions (MFS), where the source nodes <span><math><mi>Q</mi></math></span> are also located on <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span>. The error analysis of the MFS in Dou et al. (2020) , Li (2009), Li et al. (2023) is confined to circular/elliptic pseudo-boundaries. The error analysis of the MFS for non-circular/non-elliptic pseudo-boundaries can be obtained from this paper. Since the pseudo-boundary <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span> is different from the boundary <span><math><mi>Γ</mi></math></span> in the conventional BIEM, the inf-sup lemma is different from that in the boundary element method (BEM). The first work is to prove the new inf-sup lemma. For polygonal domains, when polygonal pseudo-boundaries are chosen, the piecewise interpolation polynomials of low orders are used as in the finite element method (FEM) and the BEM. The error bounds are derived for smooth solutions to achieve the optimal convergence rates. This error analysis is also valid for smooth <span><math><mi>Γ</mi></math></span>, and the constant/linear and linear/quadratic elements may find wide applications. The error analysis can also be applied to the MFS. Numerical experiments are reported to verify the analysis made. This paper is essential to the error analysis of both the DBIEM and the MFS.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117135"},"PeriodicalIF":2.6,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269742","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}

{"title":"Numerical modelling of one dimensional problems for the shallow water equations on an adaptive moving meshes","authors":"K.E. Shilnikov","doi":"10.1016/j.cam.2025.117134","DOIUrl":"10.1016/j.cam.2025.117134","url":null,"abstract":"<div><div>This work is devoted to an approach for the quality improvement of numerical solving of initial-boundary problems for one-dimensional shallow water equations on an adaptive mesh. A Godunov type numerical scheme for the problem on moving mesh is applied. The grid motion law is based on the solution of the local Riemann discontinuity breakdown problem and forces the computational nodes to follow the wave of the greatest amplitude. The regularization mechanism prevents the degeneration of moving computational mesh and gives an estimate for the mesh compression. The proposed algorithm is tested on several typical Riemann problems with known exact solutions. The numerical experiments show that the proposed approach allows to improve the quality of the obtained numerical solution.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117134"},"PeriodicalIF":2.6,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269743","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}

{"title":"Fast converging parallel offline–online iterative multiscale mixed methods","authors":"Dilong Zhou ,&nbsp;Rafael T. Guiraldello ,&nbsp;Felipe Pereira","doi":"10.1016/j.cam.2025.117123","DOIUrl":"10.1016/j.cam.2025.117123","url":null,"abstract":"<div><div>In this work, we build upon the recently introduced Multiscale Robin Coupled Method with Oversampling and Smoothing (MRCM-OS) to develop two highly efficient iterative multiscale methods. The MRCM-OS methodology demonstrated the ability to achieve flux error magnitudes on the order of <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math></span> in a challenging industry benchmark, namely the SPE10 permeability field. The two newly proposed iterative procedures, through the construction of online informed spaces, significantly enhance the solution accuracy, reaching flux error magnitudes of order <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>10</mn></mrow></msup></mrow></math></span> for a reduced number of steps.</div><div>The proposed methods are based on the construction of online informed spaces, which are iteratively refined to improve solution accuracy. Following an initial offline stage, where known boundary conditions are applied to construct multiscale basis functions, the informed spaces are updated through iterative procedures that utilize boundary conditions defined by the most recently computed solution variables. Two distinct approaches are introduced, each leveraging this framework to deliver efficient and accurate iterative solutions.</div><div>A series of numerical simulations, conducted on the SPE10 benchmark, demonstrates the very rapid convergence of the iterative solutions. These results highlight the computational efficiency and competitiveness of the two proposed methods, which are thoroughly compared to each other and to an existing multiscale iterative method from the literature.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117123"},"PeriodicalIF":2.6,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269515","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}

{"title":"Development and analysis of an equivalent Drude metamaterial perfectly matched layer model","authors":"Yunqing Huang ,&nbsp;Jichun Li ,&nbsp;Lei Xu ,&nbsp;Haoke Zhao","doi":"10.1016/j.cam.2025.117128","DOIUrl":"10.1016/j.cam.2025.117128","url":null,"abstract":"<div><div>This paper focuses on a perfectly matched layer (PML) model developed by Bécache et al. [6] for Drude metamaterials. Although this PML model performs well in practice — exhibiting stable behavior and effectively absorbing outgoing waves — its stability has not yet been rigorously proven for general damping coefficients. To address this gap, we derive an equivalent PML model from the original formulation and establish its stability under general damping functions. We then develop a finite element scheme to solve the equivalent PML model and provide proofs for both its discrete stability and optimal error estimates. Finally, we present numerical results to support our theoretical analysis and to demonstrate the effectiveness of the equivalent PML model in absorbing outgoing waves.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117128"},"PeriodicalIF":2.6,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269746","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}

{"title":"Exactly divergence-free ultra-weak discontinuous Galerkin method for Brinkman–Forchheimer equations","authors":"Zhengyang Xue ,&nbsp;Fengna Yan ,&nbsp;Yinhua Xia","doi":"10.1016/j.cam.2025.117124","DOIUrl":"10.1016/j.cam.2025.117124","url":null,"abstract":"<div><div>This paper presents an exactly divergence-free ultra-weak discontinuous Galerkin (UWDG) method, utilizing <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mtext>div</mtext><mo>)</mo></mrow></mrow></math></span>-conforming spaces for the Brinkman–Forchheimer equations. We also develop an unconditionally stable first-order time discretization scheme based on the linearized convex-splitting approach by interpreting the Brinkman–Forchheimer equations as an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> gradient flow in the exactly divergence-free space. It is proven that the fully discrete scheme remains unconditionally stable in both the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm and the energy functional, with corresponding error estimates provided. Furthermore, we employ the IMEX-BDF method with the deferred correction (DC) approach to develop high-order linear semi-implicit schemes. Numerical experiments with various parameter configurations validate the proposed schemes, demonstrating their accuracy, stability, and computational efficiency. These results underscore the robustness and effectiveness of the method in solving the Brinkman–Forchheimer equation.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"477 ","pages":"Article 117124"},"PeriodicalIF":2.6,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145277938","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}

{"title":"Development of an accurate and robust numerical scheme for simulating all Mach number flows","authors":"Lijun Hu ,&nbsp;Lielong Li ,&nbsp;Kexin Zhu ,&nbsp;Haizhuan Yuan","doi":"10.1016/j.cam.2025.117133","DOIUrl":"10.1016/j.cam.2025.117133","url":null,"abstract":"<div><div>The HLLEM scheme is a popular numerical method for computing the convective fluxes in the Euler equations and the Navier–Stokes equations due to its accuracy and positivity-preserving. However, it still has two defects. One is the numerical instability, such as the carbuncle phenomenon, in computations involving multidimensional strong shock waves; the other is the non-physical results caused by accuracy issues in computations of low Mach number flows. In the engineering field, high Mach number flows with strong shock waves and low Mach number flows often coexist. Therefore, it is necessary to develop a numerical scheme that is both accurate and robust across all Mach number flows. The shock instabilities of the HLLEM scheme are addressed by simply modifying the wave speeds to balance advection dissipation and acoustic dissipation. Additionally, the performance in computing low-speed flows is improved by controlling the excessive numerical dissipation corresponding to the velocity-difference terms in the momentum equations. Numerical results from high Mach number test cases and low Mach number test cases demonstrate the accuracy and robustness of the proposed scheme for simulating flows across all Mach number.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117133"},"PeriodicalIF":2.6,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269735","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}

{"title":"Optimal-rate error estimates and a twice decoupled solver for a backward Euler finite element scheme of the Doyle–Fuller–Newman model of lithium-ion cells","authors":"Shu Xu ,&nbsp;Liqun Cao","doi":"10.1016/j.cam.2025.117131","DOIUrl":"10.1016/j.cam.2025.117131","url":null,"abstract":"<div><div>We investigate the convergence of a backward Euler finite element discretization applied to a multi-domain and multi-scale elliptic–parabolic system, derived from the Doyle-Fuller-Newman model for lithium-ion cells. We establish optimal-order error estimates for the solution in the norms <span><math><mrow><msup><mrow><mi>l</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><msup><mrow><mi>l</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>q</mi></mrow></msubsup><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>q</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn></mrow></math></span>. To improve computational efficiency, we propose a novel solver that accelerates the solution process and controls memory usage. Numerical experiments with realistic battery parameters validate the theoretical error rates and demonstrate the significantly superior performance of the proposed solver over existing solvers.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117131"},"PeriodicalIF":2.6,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269510","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}

{"title":"Higher-degree rectangular immersed finite elements discontinuous Galerkin methods for elliptic interface problems","authors":"Qiao Zhuang ,&nbsp;Zhongqiang Zhang ,&nbsp;Marcus Sarkis ,&nbsp;Tao Lin","doi":"10.1016/j.cam.2025.117126","DOIUrl":"10.1016/j.cam.2025.117126","url":null,"abstract":"<div><div>We propose and analyze higher-degree rectangular immersed finite elements (IFE) for elliptic interface problems. These IFE functions are constructed by a Cauchy extension. Properties of the proposed IFE functions are analyzed, including the optimal approximation capability of the resulting IFE spaces, as well as inverse and trace inequalities. The higher-degree rectangular IFE spaces are employed in discontinuous Galerkin (DG) formulations to solve the elliptic interface problems. The optimal error estimates for the proposed DGIFE methods in both an energy and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norms are derived. Numerical results are provided to illustrate the convergence of the proposed DGIFE methods.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117126"},"PeriodicalIF":2.6,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269511","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}