Computers & Mathematics with Applications最新文献

{"title":"Enhancing accuracy with an adaptive discretization for the non-local integro-partial differential equations involving initial time singularities","authors":"Sudarshan Santra,&nbsp;Ratikanta Behera","doi":"10.1016/j.camwa.2025.05.019","DOIUrl":"10.1016/j.camwa.2025.05.019","url":null,"abstract":"<div><div>This work aims to construct an efficient and highly accurate numerical method to address the time singularity at <span><math><mi>t</mi><mo>=</mo><mn>0</mn></math></span> involved in a class of time-fractional parabolic integro-partial differential equations in one and two dimensions. The <em>L</em>2-<span><math><msub><mrow><mn>1</mn></mrow><mrow><mi>σ</mi></mrow></msub></math></span> scheme is used to discretize the time-fractional operator, whereas a modified version of the composite trapezoidal approximation is employed to discretize the Volterra operator in time. Subsequently, it helps to convert the proposed model into a second-order boundary value problem in a semi-discrete form. The multi-dimensional Haar wavelets are then used for grid adaptation and efficient computations for the two-dimensional problem, whereas the standard second-order approximations are employed to approximate the spatial derivatives for the one-dimensional case. The stability analysis is carried out on an adaptive mesh in time. The convergence analysis leads to <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>M</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>)</mo></math></span> accurate solution in the space-time domain for the one-dimensional problem having time singularity based on the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> norm for a suitable choice of the grading parameter. Furthermore, it provides <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>M</mi></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo>)</mo></math></span> accurate solution for the two-dimensional problem having unbounded time derivative at <span><math><mi>t</mi><mo>=</mo><mn>0</mn></math></span>. The analysis also highlights a higher order accuracy for a sufficiently smooth solution resides in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>(</mo><msub><mrow><mover><mrow><mi>Ω</mi></mrow><mo>‾</mo></mover></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></math></span> even if the mesh is discretized uniformly. The truncation error estimates for the time-fractional operator, integral operator, and spatial derivatives are presented. In addition, we have examined the impact of various parameters on the robustness and accuracy of the proposed method. Numerous tests are performed on several examples in support of the theoretical analysis. The advancement of the proposed methodology is demonstrated through the application of the time-fractional Fokker-Planck equation and the fractional-order viscoelastic dynamics having weakly singular kernels. It also confirms the superiority of the proposed method compared with existing approaches available in the literature.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"192 ","pages":"Pages 212-239"},"PeriodicalIF":2.9,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144137670","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":"A Nitsche's extended nonconforming virtual element method for biharmonic PDEs involving interfaces","authors":"Guodong Ma ,&nbsp;Jinru Chen ,&nbsp;Feng Wang","doi":"10.1016/j.camwa.2025.05.016","DOIUrl":"10.1016/j.camwa.2025.05.016","url":null,"abstract":"<div><div>In this paper, a Nitsche's extended nonconforming virtual element method is presented to discretize biharmonic PDEs involving interfaces with a more general interface condition. By introducing some special terms on cut edges and uncut edges of interface elements, we prove the well-posedness and optimal convergence, which are independent of the location of the interface relative to the mesh and the material parameter quotient. Finally, numerical experiments are carried out to verify theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"192 ","pages":"Pages 134-154"},"PeriodicalIF":2.9,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107225","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":"Non-intrusive least-squares functional a posteriori error estimator: Linear and nonlinear problems with plain convergence","authors":"Ziyan Li,&nbsp;Shun Zhang","doi":"10.1016/j.camwa.2025.05.011","DOIUrl":"10.1016/j.camwa.2025.05.011","url":null,"abstract":"<div><div>The a posteriori error estimator using the least-squares functional can be used for adaptive mesh refinement and error control even if the numerical approximations are not obtained from the corresponding least-squares method. This suggests the development of a versatile non-intrusive a posteriori error estimator. In this paper, we present a systematic approach for applying the least-squares functional error estimator to linear and nonlinear problems that are not solved by the least-squares finite element methods. For the case of an elliptic PDE solved by the standard conforming finite element method, we minimize the least-squares functional with conforming approximation inserted to recover the other physically meaningful variable. By combining the numerical approximation from the original method with the auxiliary recovery approximation, we construct the least-squares functional a posteriori error estimator. Furthermore, we introduce a new interpretation that views the non-intrusive least-squares functional error estimator as an estimator for the combined solve-recover process. This simplifies the reliability and efficiency analysis. We extend the idea to a model nonlinear problem. Plain convergence results are established for adaptive algorithms of the general second order elliptic equation and a model nonlinear problem with the non-intrusive least-squares functional a posteriori error estimators.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"191 ","pages":"Pages 275-295"},"PeriodicalIF":2.9,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116930","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":"Adaptive 3D multi-patch isogeometric analysis with truncated hierarchical NURBS for complex elasticity","authors":"Lin Wang ,&nbsp;Sundararajan Natarajan ,&nbsp;Weihua Fang ,&nbsp;Zhanfei Si ,&nbsp;Tiantang Yu","doi":"10.1016/j.camwa.2025.05.010","DOIUrl":"10.1016/j.camwa.2025.05.010","url":null,"abstract":"<div><div>A novel adaptive multi-patch isogeometric approach based on truncated hierarchical NURBS (TH-NURBS) is proposed for modeling three-dimensional elasticity. The TH-NURBS are rational extension of truncated hierarchical B-splines (THB-splines) and the salient feature of the TH-NURBS is that it can exactly model complex-shaped geometries. Owing to the properties of local refinement, partition-of-unity and linear independence, TH-NURBS are very suitable for an adaptive isogeometric analysis. The multi-patch modeling technique is used to exactly represent arbitrarily complex-shaped geometries, and the Nitsche's method is employed to maintain the continuity of variables at the coupling interface of non-conforming meshes. An automatic remeshing technique is developed based a recovery-based error estimator utilizing TH-NURBS. Several three-dimensional examples are presented that demonstrates the robustness and the accuracy of the proposed framework. From the systematic numerical study, it is opined that the proposed framework yields accurate results at lower computational cost.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"192 ","pages":"Pages 104-133"},"PeriodicalIF":2.9,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107224","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":"Preconditioning of the generalized Stokes problem arising from the approximation of the time-dependent Navier-Stokes equations","authors":"Melvin Creff,&nbsp;Jean-Luc Guermond","doi":"10.1016/j.camwa.2025.05.001","DOIUrl":"10.1016/j.camwa.2025.05.001","url":null,"abstract":"<div><div>The paper compares standard iterative methods for solving the generalized Stokes problem arising from the time and space approximation of the time-dependent incompressible Navier-Stokes equations. Various preconditioning techniques are considered: (1) pressure Schur complement; (2) fully coupled system using an exact factorization as a basis for the preconditioner; (3) fully coupled system using norm equivalence considerations as a basis for the preconditioner; (4) in all the cases we also investigate the benefits of the augmented Lagrangian formulation. Our objective is to see whether one of these methods can compete with traditional pressure-correction and velocity-correction methods in terms of throughput (the throughput is the ratio of the number of degrees of freedom of the problem divided by the number of cores and the wall-clock time in second). Numerical tests on fine unstructured meshes (68 millions degrees of freedoms) demonstrate GMRES/CG convergence rates that are independent of the mesh size and improve with the Reynolds number for most methods. Three conclusions are drawn: (1) The throughputs of all the methods tested in the paper are similar up to mesh-independent multiplicative constants (see Fig. 6). (2) Although very good parallel scalability is observed for the augmented Lagrangian version of the generalized Stokes problem, the best throughputs are achieved without the augmented Lagrangian term. (3) The throughput of all the methods tested in the paper is on average 5 to 25 times slower than that of traditional pressure-correction and velocity-correction methods (on average 5 for the best one). Hence, although all these methods are very efficient for solving steady state problems, pressure-correction and velocity-correction methods are still faster for solving time-dependent problems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"191 ","pages":"Pages 255-274"},"PeriodicalIF":2.9,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144105612","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":"Bayesian recovery of time-varying fractional order in time-fractional diffusion equations for shale gas applications","authors":"Mohamed BenSalah","doi":"10.1016/j.camwa.2025.05.015","DOIUrl":"10.1016/j.camwa.2025.05.015","url":null,"abstract":"<div><div>This work addresses the inverse problem of recovering the time-varying fractional order <span><math><mi>α</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> in a time-fractional diffusion equation, motivated by applications in subsurface flows and shale gas extraction. The fractional order <span><math><mi>α</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> plays a crucial role in modeling anomalous diffusion processes, such as those observed in complex geological formations. Prior to developing the reconstruction method, the uniqueness of the solution is analyzed, ensuring that the fractional order can be uniquely determined from the available space-averaged data. Following this theoretical investigation, a Bayesian approach is proposed to recover <span><math><mi>α</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> from space-averaged measurements, which are practical and robust against noise. The Bayesian framework allows for both parameter estimation and uncertainty quantification, making it a powerful tool for handling ill-posed inverse problems. Numerical experiments validate the approach, demonstrating accurate recovery of the fractional order and robustness in the presence of noise.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"191 ","pages":"Pages 228-244"},"PeriodicalIF":2.9,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144098559","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":"Multigrid method with greedy partial block Jacobi smoother for solving two-dimensional space-fractional diffusion equations","authors":"Kang-Ya Lu ,&nbsp;Xiao-Yun Zhang","doi":"10.1016/j.camwa.2025.05.012","DOIUrl":"10.1016/j.camwa.2025.05.012","url":null,"abstract":"<div><div>Based on the block Jacobi splitting, a kind of <em>greedy partial block Jacobi</em> (<strong>GPBJ</strong>) iteration method is constructed by greedily selecting the blocks with relatively large residuals and performing the block Jacobi iteration on the selected blocks. Theoretical analysis demonstrates that the GPBJ iteration is unconditionally convergent if the coefficient matrix of the linear system is <em>H</em>-matrix. Then combining with the alternating direction strategy, the GPBJ smoothed multigrid method is designed to solve the discrete linear system of two-dimensional space-fractional diffusion equations, where the coefficient matrix is strictly diagonally dominant. Numerical experiments indicate that the multigrid method smoothed by the GPBJ iteration can significantly reduce the computation time for solving the considered discrete linear system.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"191 ","pages":"Pages 245-254"},"PeriodicalIF":2.9,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144105611","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-order three-scale asymptotic model and efficient two-stage numerical algorithm for transient nonlinear thermal conduction problems of composite structures","authors":"Hao Dong ,&nbsp;Yanqi Wang ,&nbsp;Changqing Ye ,&nbsp;Yihan Nie ,&nbsp;Puyang Gao","doi":"10.1016/j.camwa.2025.05.009","DOIUrl":"10.1016/j.camwa.2025.05.009","url":null,"abstract":"<div><div>The accurate thermal analysis of composite structures remains a challenging issue due to complicated multiscale configurations and nonlinear temperature-dependent behaviors. This work offers a novel higher-order three-scale asymptotic (HOTSA) model and corresponding numerical algorithm for accurately and efficiently simulating transient nonlinear thermal conduction problems of heterogeneous structures with three-scale spatial hierarchy. Firstly, by recursively macro-meso and meso-micro two-scale asymptotic analysis, the macro-meso-micro correlative HOTSA model is established with higher-order cell functions and higher-order correction terms. Then, a rigorous error estimation of the HOTSA model is presented under some assumptions in the point-wise and integral sense. Furthermore, a two-stage numerical algorithm with offline micro-meso computation and online macro-multiscale computation is developed to implement efficient and high-accuracy thermal simulation for heterogeneous structures with three-level spatial scales. Finally, numerical experiments are conducted to assess the efficiency and accuracy of the proposed HOTSA model and two-stage algorithm. This study establishes a reliable higher-order three-scale computational framework, that has a great potential for accurately capturing the microscopic oscillatory information of composite structures along with a drastic reduction in the computation resource.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"192 ","pages":"Pages 72-103"},"PeriodicalIF":2.9,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090657","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":"Unconditionally energy-stable discontinuous Galerkin method for the dynamics model of protein folding","authors":"Dan Zhang ,&nbsp;YuXing Zhang ,&nbsp;Bo Wang","doi":"10.1016/j.camwa.2025.05.002","DOIUrl":"10.1016/j.camwa.2025.05.002","url":null,"abstract":"<div><div>In this paper, we present the coupled nonlinear Schrödinger equations to describe the conformational dynamics of protein secondary structure. We first construct a structure-preserving discrete scheme that ensures both mass conservation and energy stability. The proposed scheme is employed by combining the discontinuous Galerkin (DG) method for spatial discretization, Crank-Nicolson (C-N) approximation for temporal discretization, a second-order convex-concave splitting for the double-well potential and adding additional stabilization term. Moreover, by using the Brouwer fixed point theorem and the Gagliardo-Nirenberg inequality, we rigorously prove the unique solvability and convergence with second-order accuracy in both time and space without the grid ratio condition. Finally, numerical experiments are carried out to demonstrate the convergence rate, mass conservation, energy stability and performance of the developed scheme.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"192 ","pages":"Pages 14-36"},"PeriodicalIF":2.9,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084329","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 convergence analysis of an energy dissipation property virtual element method for the nonlinear Benjamin-Bona-Mahony-Burgers equation","authors":"Yanping Chen ,&nbsp;Wanxiang Liu ,&nbsp;Fangfang Qin ,&nbsp;Qin Liang","doi":"10.1016/j.camwa.2025.05.003","DOIUrl":"10.1016/j.camwa.2025.05.003","url":null,"abstract":"<div><div>A novel arbitrary high-order energy-stable fully discrete schemes are proposed for the nonlinear Benjamin-Bona-Mahony-Burgers equation based on linearized Crank-Nicolson scheme in time and the virtual element discretization in space. Two skew-symmetric discrete forms are introduced to preserve energy dissipation of the numerical scheme. Furthermore, by utilizing the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> projection to approximate the nonlinear term and estimating the error of the discrete bilinear forms carefully, the optimal error estimate of the numerical scheme in the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm is obtained. Finally, several numerical examples on various mesh types are provided to demonstrate the energy stability, optimal convergence and high efficiency of the method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"192 ","pages":"Pages 37-53"},"PeriodicalIF":2.9,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084330","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}