Pub Date : 2026-07-01Epub Date: 2026-01-29DOI: 10.1016/j.cnsns.2026.109807
Xin Liao, Lele Wang, Huaijun Yang
In this paper, based on the method of order reduction in time, an energy-conservative modified Crank-Nicolson Galerkin scheme is proposed and the unconditionally superconvergent error analysis is investigated for the nonlinear Schrödinger equation with wave operator in two dimensions. The existence and uniqueness of numerical solution are discussed. Unlike the boundedness of numerical solutions in L∞-norm used in the previous work, the key to our analysis is to novelly employ the boundedness of the numerical solution in H1-norm derived from the energy-conservative property to deal with the nonlinear term strictly and skillfully. By means of the high accuracy estimate of the bilinear element on the rectangular mesh,the unconditionally superclose error estimate is obtained without any restrictions on the ratio of temporal-spatial step-szie. Furthermore, the unconditionally superconvergence error estimate is acquired by an interpolation post-processing approach. Finally, numerical experiments are carried out to demonstrate the expected accuracy and conservation of proposed schemes.
{"title":"Unconditionally superconvergent error analysis of an energy-conservative Galerkin method for the nonlinear Schrödinger equation with wave operator","authors":"Xin Liao, Lele Wang, Huaijun Yang","doi":"10.1016/j.cnsns.2026.109807","DOIUrl":"10.1016/j.cnsns.2026.109807","url":null,"abstract":"<div><div>In this paper, based on the method of order reduction in time, an energy-conservative modified Crank-Nicolson Galerkin scheme is proposed and the unconditionally superconvergent error analysis is investigated for the nonlinear Schrödinger equation with wave operator in two dimensions. The existence and uniqueness of numerical solution are discussed. Unlike the boundedness of numerical solutions in <em>L</em><sup>∞</sup>-norm used in the previous work, the key to our analysis is to novelly employ the boundedness of the numerical solution in <em>H</em><sup>1</sup>-norm derived from the energy-conservative property to deal with the nonlinear term strictly and skillfully. By means of the high accuracy estimate of the bilinear element on the rectangular mesh,the unconditionally superclose error estimate is obtained without any restrictions on the ratio of temporal-spatial step-szie. Furthermore, the unconditionally superconvergence error estimate is acquired by an interpolation post-processing approach. Finally, numerical experiments are carried out to demonstrate the expected accuracy and conservation of proposed schemes.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109807"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072037","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}
Pub Date : 2026-07-01Epub Date: 2026-01-28DOI: 10.1016/j.cnsns.2026.109785
Grace Nnennaya Ogwo , Habib ur Rehman , Jen-Chih Yao
In this paper, we investigate the variational inequality problem with fixed-point constraints. We propose and analyze an inertial subgradient extragradient method for approximating a common solution to a quasimonotone variational inequality problem and a fixed-point problem of an infinite family of relatively nonexpansive mappings. The study is conducted in the context of a real 2-uniformly convex and uniformly smooth Banach space. Under standard assumptions, we establish a strong convergence result. Finally, we provide numerical experiments to demonstrate the effectiveness and applicability of the proposed method. Our results complement several existing methods in the literature.
{"title":"Inertial subgradient–extragradient schemes for variational inequalities in 2-uniformly convex spaces","authors":"Grace Nnennaya Ogwo , Habib ur Rehman , Jen-Chih Yao","doi":"10.1016/j.cnsns.2026.109785","DOIUrl":"10.1016/j.cnsns.2026.109785","url":null,"abstract":"<div><div>In this paper, we investigate the variational inequality problem with fixed-point constraints. We propose and analyze an inertial subgradient extragradient method for approximating a common solution to a quasimonotone variational inequality problem and a fixed-point problem of an infinite family of relatively nonexpansive mappings. The study is conducted in the context of a real 2-uniformly convex and uniformly smooth Banach space. Under standard assumptions, we establish a strong convergence result. Finally, we provide numerical experiments to demonstrate the effectiveness and applicability of the proposed method. Our results complement several existing methods in the literature.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109785"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072060","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}
Pub Date : 2026-07-01Epub Date: 2026-02-07DOI: 10.1016/j.cnsns.2026.109820
Zubair Ahmad , Angelamaria Cardone , Francesco Giannino , Gerardo Toraldo
Vegetation ring formation is a spatial pattern observed in ecosystems influenced by plant-soil negative feedback. Classical integer-order models capture only instantaneous interactions and cannot represent the history-dependent processes shaping these dynamics. To overcome this limitation, we propose a new time-fractional reaction-diffusion problem, that extends the model of Cartenì et al. of 2012 [1], by incorporating memory effects through Caputo derivatives. The system, consisting of coupled fractional partial differential equations (FPDEs) for biomass and toxicity, is analyzed for existence and uniqueness of solutions, equilibrium states, and stability in both homogeneous and heterogeneous cases. Since the analytical solution is not available, a numerical approach has been proposed. The numerical experiments illustrate variations in ring formation throughout time and space. The study covers multiple aspects, such as the influence of the fractional derivation index κ on pattern formation, showing that when κ decreases, the biomass spreads over a larger area with fewer oscillations and amplitudes. Moreover, reducing κ has the effect of slowing down the dynamics, requiring more time to reach the equilibrium points, and causes the ring’s width to expand, which shrinks the internal ring diameter until only disks are visible as κ tends to 0.6.
{"title":"Analysis and numerical simulations of fractional order model of ring formation due to plant-soil negative feedback","authors":"Zubair Ahmad , Angelamaria Cardone , Francesco Giannino , Gerardo Toraldo","doi":"10.1016/j.cnsns.2026.109820","DOIUrl":"10.1016/j.cnsns.2026.109820","url":null,"abstract":"<div><div>Vegetation ring formation is a spatial pattern observed in ecosystems influenced by plant-soil negative feedback. Classical integer-order models capture only instantaneous interactions and cannot represent the history-dependent processes shaping these dynamics. To overcome this limitation, we propose a new time-fractional reaction-diffusion problem, that extends the model of Cartenì et al. of 2012 [1], by incorporating memory effects through Caputo derivatives. The system, consisting of coupled fractional partial differential equations (FPDEs) for biomass and toxicity, is analyzed for existence and uniqueness of solutions, equilibrium states, and stability in both homogeneous and heterogeneous cases. Since the analytical solution is not available, a numerical approach has been proposed. The numerical experiments illustrate variations in ring formation throughout time and space. The study covers multiple aspects, such as the influence of the fractional derivation index <em>κ</em> on pattern formation, showing that when <em>κ</em> decreases, the biomass spreads over a larger area with fewer oscillations and amplitudes. Moreover, reducing <em>κ</em> has the effect of slowing down the dynamics, requiring more time to reach the equilibrium points, and causes the ring’s width to expand, which shrinks the internal ring diameter until only disks are visible as <em>κ</em> tends to 0.6.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109820"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134756","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}
Pub Date : 2026-07-01Epub Date: 2026-02-05DOI: 10.1016/j.cnsns.2026.109791
Dongxiang Chen, Qian He, Xiaoli Chen
This paper focuses on the hydrostatic approximation for the two-dimensional micropolar fluid system in a thin strip domain. We first establish the global well-posedness of a scaled anisotropic micropolar fluid system and the hydrostatic micropolar fluid system in a two-dimensional strip domain, under the assumption that the initial data are analytic and sufficiently small in the tangential variable. We then rigorously justify the convergence from the anisotropic system to the hydrostatic system within the analytic framework.
{"title":"On the hydrostatic approximation of the micropolar fluid system in a thin strip domain","authors":"Dongxiang Chen, Qian He, Xiaoli Chen","doi":"10.1016/j.cnsns.2026.109791","DOIUrl":"10.1016/j.cnsns.2026.109791","url":null,"abstract":"<div><div>This paper focuses on the hydrostatic approximation for the two-dimensional micropolar fluid system in a thin strip domain. We first establish the global well-posedness of a scaled anisotropic micropolar fluid system and the hydrostatic micropolar fluid system in a two-dimensional strip domain, under the assumption that the initial data are analytic and sufficiently small in the tangential variable. We then rigorously justify the convergence from the anisotropic system to the hydrostatic system within the analytic framework.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109791"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134768","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}
Pub Date : 2026-07-01Epub Date: 2026-02-05DOI: 10.1016/j.cnsns.2026.109817
R. Vanitha , T. Satheesh , V.T. Elayabharath , Y. Ren , R. Sakthivel
This article examines the output tracking and disturbance rejection issue of fractional-order Takagi-Sugeno fuzzy switched control systems with state delay, uncertainties, and external disturbance with the assistance of a parallel-equivalent-input-disturbance estimator and a two-dimensional multi-periodic modified repetitive controller. First and foremost, the parallel-equivalent-input-disturbance concept has been laid out with the intention of minimizing the occurrence of disturbance estimation errors, wherein these errors are deemed as artificial disturbances, and an array of equivalent-input-disturbance compensator have been implemented in order to make up for them. Meanwhile, in the framework of proportional integral observer, a variable for relaxation is encompassed, thereby enhancing the precision of the disturbance estimation. Subsequently, by unifying the two-dimensional multi-periodic modified repetitive controller approach with the data gleaned from the proportional integral observer and parallel-equivalent-input-disturbance, cohesive disturbance rejection-based tracking control is built, which ensures effective tracking performance while suppressing the detrimental effects of disturbances on the system. Moreover, in light of Lyapunov stability theory, an adequate set of constraints is derived in terms of linear-matrix inequalities to assure desirable outcomes. Ultimately, numerical simulation results are shown to verify the potency of the offered control scheme.
{"title":"Disturbance estimator-based tracking control for fractional-order Takagi-Sugeno fuzzy switched control systems","authors":"R. Vanitha , T. Satheesh , V.T. Elayabharath , Y. Ren , R. Sakthivel","doi":"10.1016/j.cnsns.2026.109817","DOIUrl":"10.1016/j.cnsns.2026.109817","url":null,"abstract":"<div><div>This article examines the output tracking and disturbance rejection issue of fractional-order Takagi-Sugeno fuzzy switched control systems with state delay, uncertainties, and external disturbance with the assistance of a parallel-equivalent-input-disturbance estimator and a two-dimensional multi-periodic modified repetitive controller. First and foremost, the parallel-equivalent-input-disturbance concept has been laid out with the intention of minimizing the occurrence of disturbance estimation errors, wherein these errors are deemed as artificial disturbances, and an array of equivalent-input-disturbance compensator have been implemented in order to make up for them. Meanwhile, in the framework of proportional integral observer, a variable for relaxation is encompassed, thereby enhancing the precision of the disturbance estimation. Subsequently, by unifying the two-dimensional multi-periodic modified repetitive controller approach with the data gleaned from the proportional integral observer and parallel-equivalent-input-disturbance, cohesive disturbance rejection-based tracking control is built, which ensures effective tracking performance while suppressing the detrimental effects of disturbances on the system. Moreover, in light of Lyapunov stability theory, an adequate set of constraints is derived in terms of linear-matrix inequalities to assure desirable outcomes. Ultimately, numerical simulation results are shown to verify the potency of the offered control scheme.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109817"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134760","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}
Pub Date : 2026-07-01Epub Date: 2026-02-06DOI: 10.1016/j.cnsns.2026.109800
Jie Kong , Bo Zhao
This article investigates the secure containment control problem for switched nonlinear stochastic multi-agent systems (MASs) by using the mode-dependent average dwell time (MDADT) method. As a class of cyber-physical systems, MASs are vulnerable to denial of service (DoS) attacks, which can greatly degrade the control performance or even influence the stability of controlled systems. By combining the backstepping method, a secure containment control method is developed with the event-triggering mechanism. Based on the connectivity information between communication links, this method eliminates the effects of DoS attacks. In the backstepping recursive design process, the problem of “explosion of complexity” caused by the derivation of virtual control is addressed by introducing a command filter. Additionally, the event-triggering mechanism is designed in the backstepping process to effectively save the communication resources. Then, the event-triggered secure containment control policy is derived to ensure the stability of single follower and MASs under synchronous and asynchronous switchings. The followers led by multiple leaders eventually enter and keep moving in the convex hull composed of leaders. A simulation example demonstrates the effectiveness of the present secure containment control scheme.
{"title":"Secure containment control for switched nonlinear stochastic multi-agent systems under denial of service attacks","authors":"Jie Kong , Bo Zhao","doi":"10.1016/j.cnsns.2026.109800","DOIUrl":"10.1016/j.cnsns.2026.109800","url":null,"abstract":"<div><div>This article investigates the secure containment control problem for switched nonlinear stochastic multi-agent systems (MASs) by using the mode-dependent average dwell time (MDADT) method. As a class of cyber-physical systems, MASs are vulnerable to denial of service (DoS) attacks, which can greatly degrade the control performance or even influence the stability of controlled systems. By combining the backstepping method, a secure containment control method is developed with the event-triggering mechanism. Based on the connectivity information between communication links, this method eliminates the effects of DoS attacks. In the backstepping recursive design process, the problem of “explosion of complexity” caused by the derivation of virtual control is addressed by introducing a command filter. Additionally, the event-triggering mechanism is designed in the backstepping process to effectively save the communication resources. Then, the event-triggered secure containment control policy is derived to ensure the stability of single follower and MASs under synchronous and asynchronous switchings. The followers led by multiple leaders eventually enter and keep moving in the convex hull composed of leaders. A simulation example demonstrates the effectiveness of the present secure containment control scheme.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109800"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134764","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}
Pub Date : 2026-07-01Epub Date: 2026-02-03DOI: 10.1016/j.cnsns.2026.109815
Xibei Jiang, Weixin Wu
In this paper, a discrete diffusive vector-borne epidemic model in a spatially periodic patchy environment is proposed. That is, in this discrete model, all parameters exhibit periodic changes with period N. We establish the basic reproduction number and the critical wave speed c*. By the upper and lower-solution method and Schauder’s fixed theorem, the existence of periodic traveling wave solutions satisfying specific boundary conditions is established when and c ≥ c*. Additionally, the asymptotic behaviors of traveling wave solutions are given by the asymptotic spreading speed theory. By employing eigenvalue analysis of the linearized system with comparison principles, the non-existence of traveling wave solutions is established when or . The numerical simulation eventually verified the correctness of the theoretical results.
{"title":"Periodic wave propagation of a discrete diffusive vector-borne epidemic model in spatially periodic patchy environment","authors":"Xibei Jiang, Weixin Wu","doi":"10.1016/j.cnsns.2026.109815","DOIUrl":"10.1016/j.cnsns.2026.109815","url":null,"abstract":"<div><div>In this paper, a discrete diffusive vector-borne epidemic model in a spatially periodic patchy environment is proposed. That is, in this discrete model, all parameters exhibit periodic changes with period <em>N</em>. We establish the basic reproduction number <span><math><msub><mi>R</mi><mn>0</mn></msub></math></span> and the critical wave speed <em>c</em>*. By the upper and lower-solution method and Schauder’s fixed theorem, the existence of periodic traveling wave solutions satisfying specific boundary conditions is established when <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></math></span> and <em>c</em> ≥ <em>c</em>*. Additionally, the asymptotic behaviors of traveling wave solutions are given by the asymptotic spreading speed theory. By employing eigenvalue analysis of the linearized system with comparison principles, the non-existence of traveling wave solutions is established when <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>≤</mo><mn>1</mn></mrow></math></span> or <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn><mo>,</mo><mi>c</mi><mo><</mo><msup><mi>c</mi><mo>*</mo></msup></mrow></math></span>. The numerical simulation eventually verified the correctness of the theoretical results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109815"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110506","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}
Pub Date : 2026-07-01Epub Date: 2026-01-29DOI: 10.1016/j.cnsns.2026.109806
Liming Guo, Shishun Li
In this paper, we propose a second-order in time decoupled finite element method for the time-dependent Stokes-Biot problem. Our numerical scheme is a combination of the second-order backward differentiation formula and the second-order Gear’s extrapolation approach. It uncouples the original problem into two decoupled problems, the Stokes model and the Biot model. We establish the stability of the proposed fully-discrete finite element scheme in both the L2-norm and the H1-norm, and derive the corresponding error estimates. Numerical results show that our algorithm delivers faster computation and lower memory usage than monolithic methods while maintaining comparable accuracy.
{"title":"Stability and error estimates of a second-order decoupled finite element method for the time-dependent Stokes-Biot problem","authors":"Liming Guo, Shishun Li","doi":"10.1016/j.cnsns.2026.109806","DOIUrl":"10.1016/j.cnsns.2026.109806","url":null,"abstract":"<div><div>In this paper, we propose a second-order in time decoupled finite element method for the time-dependent Stokes-Biot problem. Our numerical scheme is a combination of the second-order backward differentiation formula and the second-order Gear’s extrapolation approach. It uncouples the original problem into two decoupled problems, the Stokes model and the Biot model. We establish the stability of the proposed fully-discrete finite element scheme in both the <em>L</em><sup>2</sup>-norm and the <em>H</em><sup>1</sup>-norm, and derive the corresponding error estimates. Numerical results show that our algorithm delivers faster computation and lower memory usage than monolithic methods while maintaining comparable accuracy.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109806"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071522","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}
We study a thermo–poroelastic system of coupled equations that incorporates a tempered Caputo fractional operator acting on a time–varying delay, extending previous models by including these effects. Under appropriate structural and dissipativity conditions, we establish well–posedness and prove exponential stability of the associated energy functional. A numerical scheme is constructed and tested, confirming the predicted decay rates and illustrating the influence of poroelastic damping, thermo–mechanical coupling and fractional parameters. The results show consistent agreement between theory and computation and to the best of our knowledge, this is a significant extension of previous studies in control or wave–type PDE systems, where a tempered Caputo derivative acts on a time–varying delay.
{"title":"Theoretical and numerical study of exponential stability in thermo-poroelastic systems with tempered fractional delay","authors":"Luqman Bashir , Jianghao Hao , M. Fahim Aslam , Iqra Kanwal","doi":"10.1016/j.cnsns.2026.109808","DOIUrl":"10.1016/j.cnsns.2026.109808","url":null,"abstract":"<div><div>We study a thermo–poroelastic system of coupled equations that incorporates a tempered Caputo fractional operator acting on a time–varying delay, extending previous models by including these effects. Under appropriate structural and dissipativity conditions, we establish well–posedness and prove exponential stability of the associated energy functional. A numerical scheme is constructed and tested, confirming the predicted decay rates and illustrating the influence of poroelastic damping, thermo–mechanical coupling and fractional parameters. The results show consistent agreement between theory and computation and to the best of our knowledge, this is a significant extension of previous studies in control or wave–type PDE systems, where a tempered Caputo derivative acts on a time–varying delay.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109808"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072039","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}
Pub Date : 2026-07-01Epub Date: 2026-01-29DOI: 10.1016/j.cnsns.2026.109805
Rong Hu , Dong-Ling Cai , Yi-Bin Xiao , Wei Li
In this paper, we propose a family of Moreau-Yosida regularized gap functions for variational-hemivariational inequalities, based on generalized gradients of locally Lipschitz functions. We show that the original problem is equivalent to an unconstrained, convex and continuously differentiable minimization problem. In addition, we establish global error bounds and derive a Polyak-Łojasiewicz inequality with explicit constants, which yields linear convergence of standard first-order methods. Numerical simulations are presented to illustrate the theoretical results and the predicted convergence behavior.
{"title":"Differentiable minimization problems for variational-hemivariational inequalities","authors":"Rong Hu , Dong-Ling Cai , Yi-Bin Xiao , Wei Li","doi":"10.1016/j.cnsns.2026.109805","DOIUrl":"10.1016/j.cnsns.2026.109805","url":null,"abstract":"<div><div>In this paper, we propose a family of Moreau-Yosida regularized gap functions for variational-hemivariational inequalities, based on generalized gradients of locally Lipschitz functions. We show that the original problem is equivalent to an unconstrained, convex and continuously differentiable minimization problem. In addition, we establish global error bounds and derive a Polyak-Łojasiewicz inequality with explicit constants, which yields linear convergence of standard first-order methods. Numerical simulations are presented to illustrate the theoretical results and the predicted convergence behavior.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109805"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072036","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}
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