Journal of Computational and Applied Mathematics最新文献_第3页

High-order implicit maximum-principle-preserving local discontinuous Galerkin methods for convection–diffusion equations 对流扩散方程的高阶隐式保极大原理局部不连续Galerkin方法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-12 DOI: 10.1016/j.cam.2025.116660

Kaichang Yu , Juan Cheng , Yuanyuan Liu , Chi-Wang Shu

{"title":"High-order implicit maximum-principle-preserving local discontinuous Galerkin methods for convection–diffusion equations","authors":"Kaichang Yu , Juan Cheng , Yuanyuan Liu , Chi-Wang Shu","doi":"10.1016/j.cam.2025.116660","DOIUrl":"10.1016/j.cam.2025.116660","url":null,"abstract":"<div><div>We consider maximum-principle-preserving (MPP) property of two types of implicit local discontinuous Galerkin (LDG) schemes for solving diffusion and convection–diffusion equations. The first one is the original LDG scheme proposed in Cockburn and Shu (1998) with backward Euler time discretization. The second one adds an MPP scaling limiter defined in Zhang and Shu (2010), to the first one. Compared with explicit time discretization, implicit method allows for a larger time step. For pure diffusion equations in 1D, we prove that the second type of the LDG schemes is MPP, which can also achieve high order accuracy. This result can be generalized to 2D by using tensor product meshes but only for the second order <span><math><msup><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> case. For convection–diffusion equations, the first type of LDG schemes, in the second order <span><math><msup><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> case in 1D, is proved to be MPP. In all the results above, in order to achieve the MPP property, it is necessary to have a lower bound on the time step in terms of the Courant–Friedrichs–Lewy (CFL) number. Although the analysis is only performed on linear equations, numerical experiments are provided to demonstrate that the second type of the LDG schemes works well in terms of the MPP property both for nonlinear convection–diffusion equations and for 2D higher order cases.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"470 ","pages":"Article 116660"},"PeriodicalIF":2.1,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143838896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Augmented Levin methods for vector-valued highly oscillatory integrals with exotic oscillators and turning points 具有奇异振子和拐点的向量值高振荡积分的增广Levin方法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-12 DOI: 10.1016/j.cam.2025.116687

Yinkun Wang , Shuhuang Xiang

引用次数: 0

The spectral radius of iterative methods for the Cahn–Hilliard equation and its relation to the splitting technique Cahn-Hilliard方程迭代法的谱半径及其与分裂技术的关系

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-12 DOI: 10.1016/j.cam.2025.116673

Sergei Prokopev , Alexander Nepomnyashchy , Tatyana Lyubimova

引用次数: 0

A continuous Petrov–Galerkin method for time-fractional Fokker–Planck equation 时间分数型Fokker-Planck方程的连续Petrov-Galerkin方法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-11 DOI: 10.1016/j.cam.2025.116689

Zemian Zhang , Yanping Chen , Yunqing Huang , Jian Huang , Yanping Zhou

{"title":"A continuous Petrov–Galerkin method for time-fractional Fokker–Planck equation","authors":"Zemian Zhang , Yanping Chen , Yunqing Huang , Jian Huang , Yanping Zhou","doi":"10.1016/j.cam.2025.116689","DOIUrl":"10.1016/j.cam.2025.116689","url":null,"abstract":"<div><div>A continuous Petrov–Galerkin (CPG) method for the time discretization of a time-fractional Fokker–Planck equation with a general driving force involving fractional exponent <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> is proposed. An <span><math><mi>α</mi></math></span>-robust stability bound for the time discrete solution is obtained for <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. Regarding error analysis, time-graded meshes are utilized to address the singular behavior of the continuous solution near origin. We present the nodal error estimate with non-uniform time meshes and obtain the optimal second-order accurate estimate for <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. The fully-discrete scheme by employing standard (continuous) finite element method in space is considered, and the corresponding error is estimated. Numerical experiments demonstrate that the assumptions of time-graded meshes can be further relaxed, and the results exhibit second-order accuracy for <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"470 ","pages":"Article 116689"},"PeriodicalIF":2.1,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143842837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Advantages of the Samarskii-type schemes on the Shishkin mesh 希什金网格上的萨马尔斯基类型方案的优势

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-11 DOI: 10.1016/j.cam.2025.116688

Relja Vulanović , Thái Anh Nhan

引用次数: 0

Finite element analysis of a pseudostress–pressure–velocity formulation of the stationary Navier–Stokes equations 稳态Navier-Stokes方程伪应力-压力-速度公式的有限元分析

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-10 DOI: 10.1016/j.cam.2025.116665

M. Farhloul , N. Fall , I. Dione , S. Léger

引用次数: 0

An equivalent fractional optimization problem under invexity conditions for solving fractional vector variational-like inequality problems to portfolio optimization in finance 指数条件下求解金融投资组合优化中的分数向量类变分不等式问题的等效分数优化问题

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-10 DOI: 10.1016/j.cam.2025.116684

Shubham Singh, Shalini

引用次数: 0

Composite Tseng-type extragradient algorithms with adaptive inertial correction strategy for solving bilevel split pseudomonotone VIP under split common fixed-point constraint 基于自适应惯性校正策略的复合tseng型外聚算法求解分裂公共不动点约束下的双层分裂伪单调VIP

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-09 DOI: 10.1016/j.cam.2025.116683

Lu-Chuan Ceng , Debdas Ghosh , Habib ur Rehman , Xiaopeng Zhao

{"title":"Composite Tseng-type extragradient algorithms with adaptive inertial correction strategy for solving bilevel split pseudomonotone VIP under split common fixed-point constraint","authors":"Lu-Chuan Ceng , Debdas Ghosh , Habib ur Rehman , Xiaopeng Zhao","doi":"10.1016/j.cam.2025.116683","DOIUrl":"10.1016/j.cam.2025.116683","url":null,"abstract":"<div><div>This paper investigates the bilevel split pseudomonotone variational inequality problem (BSPVIP) and the split common fixed point problem (SCFPP) involving demimetric mappings in real Hilbert spaces. We propose a novel composite Tseng-type extragradient method that incorporates an adaptive inertial correction term to effectively address the BSPVIP under the SCFPP constraints. Our approach combines an inertial technique with a self-adaptive step size strategy to enhance algorithmic efficiency. The BSPVIP consists of an upper-level variational inequality problem for a strongly monotone operator and a lower-level split variational inequality problem for two pseudomonotone operators. Under mild assumptions, we establish the strong convergence of the proposed algorithm. To demonstrate the practical applicability of the method, we apply it to a BSPVIP under split fixed point problem constraints. A numerical example is provided to illustrate the algorithm’s performance and examine the influence of the involved parameters on its behavior.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"470 ","pages":"Article 116683"},"PeriodicalIF":2.1,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143834600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Projection method for steady states of Cahn–Hilliard equation with the dynamic boundary condition 具有动态边界条件的Cahn-Hilliard方程稳态的投影法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-07 DOI: 10.1016/j.cam.2025.116674

Shuting Gu , Ming Xiao , Rui Chen

{"title":"Projection method for steady states of Cahn–Hilliard equation with the dynamic boundary condition","authors":"Shuting Gu , Ming Xiao , Rui Chen","doi":"10.1016/j.cam.2025.116674","DOIUrl":"10.1016/j.cam.2025.116674","url":null,"abstract":"<div><div>The Cahn–Hilliard equation is a fundamental model that describes phase separation processes of two-phase flows or binary mixtures. In recent years, the dynamic boundary conditions for the Cahn–Hilliard equation have been proposed and analyzed. Our first goal in this article is to present a projection method to locate the steady state of the CH equation with dynamic boundary conditions. The main feature of this method is that it only uses the variational derivative in the metric <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and not that in the metric <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span>, thus significantly reducing the computational cost. In addition, the projected dynamics fulfill the important physical properties: mass conservation and energy dissipation. In the temporal construction of the numerical schemes, the convex splitting method is used to ensure a large time step size. Numerical experiments for the two-dimensional Ginzburg–Landau free energy, where the surface potential is the double well potential or the moving contact line potential, are conducted to demonstrate the effectiveness of this projection method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116674"},"PeriodicalIF":2.1,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143792136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Robust second-order VSBDF2 finite element schemes for parabolic distributed optimal control problems 抛物型分布最优控制问题的鲁棒二阶VSBDF2有限元格式

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-07 DOI: 10.1016/j.cam.2025.116672

Caijie Yang, Tongjun Sun

{"title":"Robust second-order VSBDF2 finite element schemes for parabolic distributed optimal control problems","authors":"Caijie Yang, Tongjun Sun","doi":"10.1016/j.cam.2025.116672","DOIUrl":"10.1016/j.cam.2025.116672","url":null,"abstract":"<div><div>In this paper, we further investigate the variable-step BDF2 (VSBDF2) finite element schemes for solving control constrained distributed optimal control problems governed by parabolic equations, where the state, co-state and control variables are approximated by piecewise linear functions. We first propose the VSBDF2 backward and forward formulas, respectively. Then, motivated by the discrete orthogonal convolution (DOC) and discrete complementary convolution (DCC) backward kernels (Liao and Zhang, 2021; Zhang and Zhao, 2022), we introduce the novel DOC and DCC forward kernels. Utilizing the new analytical tool of backward and forward kernels concerning the DOC and DCC, we can obtain a priori error estimates with the optimal second-order temporal accuracy for the parabolic distributed optimal control problem under the restriction condition <span><math><mrow><mn>1</mn><mo>/</mo><mn>4</mn><mo>.</mo><mn>8645</mn><mo>⩽</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>⩽</mo><mn>4</mn><mo>.</mo><mn>8645</mn></mrow></math></span>. Moreover, our analysis also shows that the initial solutions <span><math><msup><mrow><mi>y</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>p</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span> obtained by VSBDF1 backward and forward formulas (i.e., the variable-step backward and forward Euler formulas) do not result in the loss of accuracy with <span><math><mrow><mn>1</mn><mo>/</mo><mn>4</mn><mo>.</mo><mn>8645</mn><mo>⩽</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>⩽</mo><mn>4</mn><mo>.</mo><mn>8645</mn></mrow></math></span>. Numerical experiments are provided to validate our theoretical analysis.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116672"},"PeriodicalIF":2.1,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143792137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0