Computers & Mathematics with Applications最新文献

Unconditionally maximum principle preserving scheme for the Allen–Cahn equation with a logarithmic free energy 具有对数自由能的Allen-Cahn方程的无条件最大原则保持格式

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-30 DOI: 10.1016/j.camwa.2025.07.032

Junxiang Yang , Sangkwon Kim , Junseok Kim

引用次数: 0

Formulae and transformations for simplicial tensorial finite elements via polytopal templates 通过多边形模板的简单张拉有限元的公式和变换

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-28 DOI: 10.1016/j.camwa.2025.07.028

Adam Sky , Michael Neunteufel , Jack S. Hale , Andreas Zilian

{"title":"Formulae and transformations for simplicial tensorial finite elements via polytopal templates","authors":"Adam Sky , Michael Neunteufel , Jack S. Hale , Andreas Zilian","doi":"10.1016/j.camwa.2025.07.028","DOIUrl":"10.1016/j.camwa.2025.07.028","url":null,"abstract":"<div><div>We introduce a unified method for constructing the basis functions of a wide variety of partially continuous tensor-valued finite elements on simplices using polytopal templates. These finite element spaces are essential for achieving well-posed discretisations of mixed formulations of partial differential equations that involve tensor-valued functions, such as the Hellinger–Reissner formulation of linear elasticity. In our proposed polytopal template method, the basis functions are constructed from template tensors associated with the geometric polytopes (vertices, edges, faces etc.) of the reference simplex and any scalar-valued <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-conforming finite element space. From this starting point we can construct the Regge, Hellan–Herrmann–Johnson, Pechstein–Schöberl, Hu–Zhang, Hu–Ma–Sun and Gopalakrishnan–Lederer–Schöberl elements. Because the Hu–Zhang element and the Hu–Ma–Sun element cannot be mapped from the reference simplex to a physical simplex via standard double Piola mappings, we also demonstrate that the polytopal template tensors can be used to define a consistent mapping from a reference simplex even to a non-affine simplex in the physical mesh. Finally, we discuss the implications of element regularity with two numerical examples for the Reissner–Mindlin plate problem.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 322-348"},"PeriodicalIF":2.9,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713999","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

Numerical analysis of a discontinuous Galerkin method for time-fractional Navier-Stokes-Fokker-Planck equations with weakly singular solutions 具有弱奇异解的时间分数阶Navier-Stokes-Fokker-Planck方程的不连续Galerkin方法数值分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-28 DOI: 10.1016/j.camwa.2025.07.031

Dong Liu , Weihua Deng

引用次数: 0

The two-grid decoupled method for hybrid-dimensional fracture models based on the discontinuous Galerkin method 基于不连续Galerkin方法的混合维裂缝模型双网格解耦方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-28 DOI: 10.1016/j.camwa.2025.07.029

Shuangshuang Chen, Yuna Xu, Longchao Jin

{"title":"The two-grid decoupled method for hybrid-dimensional fracture models based on the discontinuous Galerkin method","authors":"Shuangshuang Chen, Yuna Xu, Longchao Jin","doi":"10.1016/j.camwa.2025.07.029","DOIUrl":"10.1016/j.camwa.2025.07.029","url":null,"abstract":"<div><div>In this paper, we consider a kind of hybrid-dimensional fracture models, in which fractures are treated as <span><math><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-dimensional objects in a <em>n</em>-dimensional porous medium, and the interaction between fractures and surrounding domain is taken into account. For the model with one single fracture, the discontinuous Galerkin (DG) method is firstly proposed, and the optimal order error estimate in the discrete <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm for the pressure is derived. Moreover, a two-grid decoupled method is considered, which uses a coarse grid rough approximations of the interface variables to decouple the mixed domain problem on a fine grid, and the optimal error estimate is also analyzed. The proposed DG method and two-grid decoupled method are then extended to a model with complex intersecting fractures, as well as the corresponding theoretical analysis. Numerical examples with both one single fracture and intersecting fractures are all presented to verity the accuracy of the considered methods.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 296-321"},"PeriodicalIF":2.9,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713795","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

A posteriori error estimates for the DD+L2 jumps method on the neutron diffusion equations 中子扩散方程DD+L2跳变方法的后验误差估计

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-28 DOI: 10.1016/j.camwa.2025.07.026

Patrick Ciarlet , Minh Hieu Do , Mario Gervais , François Madiot

引用次数: 0

Equilibrated flux a posteriori error estimates and adaptivity for nonlinear and doubly degenerate elliptic problems 非线性和双退化椭圆型问题的平衡通量、后验误差估计和自适应

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-25 DOI: 10.1016/j.camwa.2025.07.019

Elyes Ahmed , Saber Amdouni

{"title":"Equilibrated flux a posteriori error estimates and adaptivity for nonlinear and doubly degenerate elliptic problems","authors":"Elyes Ahmed , Saber Amdouni","doi":"10.1016/j.camwa.2025.07.019","DOIUrl":"10.1016/j.camwa.2025.07.019","url":null,"abstract":"<div><div>In this work, we establish a posteriori error analysis for a class of nonlinear and doubly degenerate elliptic equations, including the Stefan problem and both fast and slow diffusion in porous media. Our analysis leverages equilibrated flux reconstructions, yielding guaranteed and fully computable upper bounds on an energy-type error norm with local efficiency. These bounds are fully computable and robust, remaining unaffected by the degree of nonlinearity and degeneracy. The proposed estimators steer an adaptive solver that dynamically switches between nonlinear solvers to optimize iterations. The adaptive algorithm addresses discretization, regularization, and linearization errors. When Newton's method encounters convergence failures, the algorithm adaptively switches to the L-scheme solver. This solver precomputes the stabilization parameter <span><math><mi>L</mi><mo>></mo><mn>0</mn></math></span> in an offline phase to approximate the Jacobian. The efficiency of the adaptive algorithm is demonstrated through four prototypical examples, showcasing its effective error control and significant computational savings.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 239-264"},"PeriodicalIF":2.9,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703834","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

Solving the second kind Volterra-Fredholm type of two-dimensional integral equations on non-rectangular domains via radial basis functions 利用径向基函数求解非矩形域上第二类Volterra-Fredholm型二维积分方程

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-25 DOI: 10.1016/j.camwa.2025.07.027

Mohsen Jalalian , Manochehr Kazemi , Mohammad Esmael Samei

引用次数: 0

Performance of a vertex-centred block-coupled finite volume methodology for small-strain static elastoplasticity 点心块耦合有限体积方法的小应变静态弹塑性性能

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-24 DOI: 10.1016/j.camwa.2025.07.020

Federico Mazzanti , Philip Cardiff

引用次数: 0

Nonlinear PDE model for pricing European options with transaction costs under the 3/2 non-affine stochastic volatility model 3/2非仿射随机波动率模型下具有交易费用的欧式期权定价的非线性PDE模型

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-23 DOI: 10.1016/j.camwa.2025.07.014

Jianguo Tan , Jiling Cao

引用次数: 0

Denoising algorithm of the modified Gray-Scott model on non-uniform grids 改进Gray-Scott模型在非均匀网格上的去噪算法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-23 DOI: 10.1016/j.camwa.2025.07.016

Shanshan Ge , Jian Wang

{"title":"Denoising algorithm of the modified Gray-Scott model on non-uniform grids","authors":"Shanshan Ge , Jian Wang","doi":"10.1016/j.camwa.2025.07.016","DOIUrl":"10.1016/j.camwa.2025.07.016","url":null,"abstract":"<div><div>This paper introduces an denoising algorithm based on the Gray-Scott (GS) model, which adopts non-uniform grids and highly adaptive numerical strategy to achieve effective denoising for two-dimensional (2D) and three-dimensional (3D) models. This method adjusts the grid density based on regional characteristics: dense grids are used in the area of interest to improve local accuracy, and sparse grids are used in non-critical areas to enhance the overall computational efficiency. In order to enhance the robustness and shape preserving ability, we modify the original GS model by replacing <span><math><mo>(</mo><mi>F</mi><mo>+</mo><mi>k</mi><mo>)</mo><mi>v</mi></math></span> with <span><math><mo>(</mo><mi>F</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>(</mo><mi>v</mi><mo>−</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math></span>, which effectively relives the volume shrinkage and shape distortion problems, and achieves the retention of structural details and effective suppression of noise. Numerical experiments show that our algorithm can maintain key geometric features while improving the smoothness, and has excellent denoising performance and extensive applicability.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 191-211"},"PeriodicalIF":2.9,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686130","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