Computers & Mathematics with Applications最新文献

{"title":"A streamline diffusion method for nonstationary incompressible magnetohydrodynamics system with variable density","authors":"Mingxia Li ,&nbsp;Qianqian Ding ,&nbsp;Shipeng Mao","doi":"10.1016/j.camwa.2025.05.020","DOIUrl":"10.1016/j.camwa.2025.05.020","url":null,"abstract":"<div><div>This paper proposes a streamline diffusion numerical method for the unsteady magnetohydrodynamic flows with variable density, in which the electric conductivity and viscosity coefficients depend on the density. We employ stable mini-elements to discretize the Navier-Stokes equations and the Nédélec edge elements to discretize the magnetic induction. In each time step, the equations for velocity and pressure are decoupled with pressure computed by solving one Poisson equation. The streamline diffusion method is applied to the continuity equation, based on which a stable finite element scheme is proposed. We show that the fully discrete numerical scheme is energy-stable and well-posed. Rigorous error estimate of all the variables is established without assuming that the density has a good approximation, which shows that this method performs as well as the constant density.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"193 ","pages":"Pages 1-19"},"PeriodicalIF":2.9,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194453","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 mixed finite element method for pricing American options and Greeks in the Heston model","authors":"Youness Mezzan ,&nbsp;Moulay Hicham Tber","doi":"10.1016/j.camwa.2025.05.023","DOIUrl":"10.1016/j.camwa.2025.05.023","url":null,"abstract":"<div><div>In this paper, we propose a numerical algorithm for solving a complementarity system associated with pricing American options. More precisely, we consider the stochastic volatility Heston's model. Our method is based on a semi-Lagrangian approach that couples mixed finite elements with a discretization of the material derivative along the characteristics. A primal dual active set solver is developed to handle the complementarity saddle point system obtained at the discrete level. To demonstrate the precision and effectiveness of our method, numerical examples are provided.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"193 ","pages":"Pages 20-33"},"PeriodicalIF":2.9,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194640","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":"Computationally efficient r−adaptive graded meshes over non-convex domains","authors":"Simone Appella,&nbsp;Chris Budd,&nbsp;Tristan Pryer","doi":"10.1016/j.camwa.2025.05.018","DOIUrl":"10.1016/j.camwa.2025.05.018","url":null,"abstract":"<div><div>This study explores the use of <em>r</em>-adaptive mesh refinement strategies for elliptic partial differential equations (PDEs) posed on non-convex domains. We introduce an <em>r</em>-adaptive strategy based on a simplified optimal transport method to create a graded mesh, distributing the interpolation error evenly, considering the solution's local asymptotic behaviour. The grading ensures good mesh compression and regularity, regardless of dimension or location. We showcase our approach by studying discontinuous Galerkin (dG) finite element approximations. We utilise a posteriori error estimates for the dG method on general meshes, showing equidistribution across our graded mesh. Numerical tests on ‘L-shaped’ and ‘crack’ domains confirm that our method achieves optimal convergence rates.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"192 ","pages":"Pages 240-258"},"PeriodicalIF":2.9,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144146887","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":"FEM for 1D-problems involving the logarithmic Laplacian: Error estimates and numerical implementation","authors":"Víctor Hernández-Santamaría ,&nbsp;Sven Jarohs ,&nbsp;Alberto Saldaña ,&nbsp;Leonard Sinsch","doi":"10.1016/j.camwa.2025.05.013","DOIUrl":"10.1016/j.camwa.2025.05.013","url":null,"abstract":"<div><div>We present the numerical analysis of a finite element method (FEM) for one-dimensional Dirichlet problems involving the logarithmic Laplacian (the pseudo-differential operator that appears as a first-order expansion of the fractional Laplacian as the exponent <span><math><mi>s</mi><mo>→</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></math></span>). Our analysis exhibits new phenomena in this setting; in particular, using recently obtained regularity results, we prove rigorous error estimates and provide a logarithmic order of convergence in the energy norm using suitable <em>log</em>-weighted spaces. Moreover, we show that the stiffness matrix of logarithmic problems can be obtained as the derivative of the fractional stiffness matrix evaluated at <span><math><mi>s</mi><mo>=</mo><mn>0</mn></math></span>. Lastly, we investigate the relationship between the discrete eigenvalue problem and its convergence to the continuous one.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"192 ","pages":"Pages 189-211"},"PeriodicalIF":2.9,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138474","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 hybrid solution method for an inverse problem for the general transport equation","authors":"Fikret Gölgeleyen ,&nbsp;Ismet Gölgeleyen ,&nbsp;Muhammed Hasdemir","doi":"10.1016/j.camwa.2025.05.014","DOIUrl":"10.1016/j.camwa.2025.05.014","url":null,"abstract":"<div><div>In this work, we deal with an inverse source problem for a general transport equation. First, we discuss the solvability of the problem. Next, in order to solve the problem, we propose a new hybrid numerical algorithm which is based on the finite difference method, Newton-Cotes formula, Lagrange polynomial approximation and composite trapezoidal rule. The proposed method is tested on several examples and the results show that the relative errors in the computation are sufficiently small and the algorithm is robust to data noises.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"192 ","pages":"Pages 172-188"},"PeriodicalIF":2.9,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138481","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":"An innovative Galerkin scheme based on anisotropic trilinear immersed finite elements for the magnetized plasma diffusion problem with plasma sheath interface","authors":"Ziping Wang ,&nbsp;Guangqing Xia ,&nbsp;Yajie Han ,&nbsp;Chang Lu ,&nbsp;Lin Zhang ,&nbsp;Gang Xu","doi":"10.1016/j.camwa.2025.05.017","DOIUrl":"10.1016/j.camwa.2025.05.017","url":null,"abstract":"<div><div>Via introducing the Robin flux jump into the Galerkin scheme, this paper develops a new anisotropic trilinear immersed finite element (IFE) method for solving the magnetized plasma diffusion problem with plasma sheath interface condition under Cartesian meshes. The three-dimensional (3D) diffusion process of magnetized plasma is anisotropic and highly sensitive to magnetic fields, making it difficult to efficiently solve by commonly used body fitted mesh methods when the simulation domain has complex boundary conditions. Even worse, the plasma sheath boundary will further exacerbates its solving difficulty. The presented method first utilizes the anisotropic trilinear IFE basis functions describing the diffusion of magnetized plasma in interface elements. Then the trilinear IFE basis functions are used to handle the plasma sheath interface conditions, i.e. the Robin flux jump conditions. As for the other non interface elements, the traditional trilinear basis functions are used. On this basis, a new Galerkin scheme is derived and applied to efficiently solving the plasma anisotropic diffusion problem with the Robin flux jump interfaces in Cartesian meshes. The proposed method can also solve other types of elliptical interface problems via controlling the coefficients. Moreover, the orthogonal meshes makes it convenient to couple other Cartesian mesh based methods, such as the particle-in-cell method, which provides an advanced tool for solving plasma transport problems. Numerical experiments are provided to demonstrate the proposed method and show the applicability in the simulations of actual engineering issues.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"192 ","pages":"Pages 155-171"},"PeriodicalIF":2.9,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134023","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":"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}