International Journal of Numerical Analysis and Modeling最新文献

$hp$-Version Analysis for Arbitrarily Shaped Elements on the Boundary Discontinuous Galerkin Method for Stokes Systems 边界上任意形状元素的 $hp$ 版本分析斯托克斯系统的连续伽勒金方法

IF 1.1 4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2024-06-01 DOI: 10.4208/ijnam2024-1021

Efthymios N. Karatzas

{"title":"$hp$-Version Analysis for Arbitrarily Shaped Elements on the Boundary Discontinuous Galerkin Method for Stokes Systems","authors":"Efthymios N. Karatzas","doi":"10.4208/ijnam2024-1021","DOIUrl":"https://doi.org/10.4208/ijnam2024-1021","url":null,"abstract":"In the present work, we examine and analyze an $hp$-version interior penalty discontinuous Galerkin finite element method for the numerical approximation of a steady fluid system on\u0000computational meshes consisting of polytopic elements on the boundary. This approach is based\u0000on the discontinuous Galerkin method, enriched by arbitrarily shaped elements techniques as has\u0000been introduced in [13]. In this framework, and employing extensions of trace, Markov-type, and $H^1/L^2$-type inverse estimates to arbitrary element shapes, we examine a stationary Stokes fluid\u0000system enabling the proof of the inf/sup condition and the $hp$- a priori error estimates, while we\u0000investigate the optimal convergence rates numerically. This approach recovers and integrates the\u0000flexibility and superiority of the discontinuous Galerkin methods for fluids whenever geometrical\u0000deformations are taking place by degenerating the edges, facets, of the polytopic elements only\u0000on the boundary, combined with the efficiency of the $hp$-version techniques based on arbitrarily\u0000shaped elements without requiring any mapping from a given reference frame.","PeriodicalId":50301,"journal":{"name":"International Journal of Numerical Analysis and Modeling","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Stabilizer-Free Weak Galerkin Finite Element Method for the Darcy-Stokes Equations 达西-斯托克斯方程的无稳定器弱 Galerkin 有限元方法

IF 1.1 4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2024-06-01 DOI: 10.4208/ijnam2024-1018

Kai He,Junjie Chen,Li Zhang, Maohua Ran

引用次数: 0

A Voigt-Regularization of the Thermally Coupled Inviscid, Resistive Magnetohydrodynamic 热耦合无粘性、电阻磁流体动力学的 Voigt 规则化

IF 1.1 4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2024-06-01 DOI: 10.4208/ijnam2024-1019

Xingwei Yang,Pengzhan Huang, Yinnian He

引用次数: 0

Mixed Virtual Element Method for Linear Parabolic Integro-Differential Equations 线性抛物线积分微分方程的混合虚拟元素法

IF 1.1 4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2024-06-01 DOI: 10.4208/ijnam2024-1020

Meghana Suthar, Sangita Yadav

引用次数: 0

Dynamics Analysis of HIV-1 Infection Model with CTL Immune Response and Delays 带有 CTL 免疫反应和延迟的 HIV-1 感染模型的动力学分析

IF 1.1 4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2024-06-01 DOI: 10.4208/ijnam2024-1022

Ting Guo, Fei Zhao

引用次数: 0

The Weak Galerkin Finite Element Method for the Dual-Porosity-Stokes Model 双孔隙-斯托克斯模型的弱伽勒金有限元法

IF 1.1 4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2024-06-01 DOI: 10.4208/ijnam2024-1023

Lin Yang,Wei Mu,Hui Peng, Xiuli Wang

引用次数: 0

A Direct Method for Solving Three-Dimensional Elliptic Interface Problems 解决三维椭圆界面问题的直接方法

IF 1.1 4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2024-05-01 DOI: 10.4208/ijnam2024-1014

Kumudu Gamage,Yan Peng, Zhilin Li

{"title":"A Direct Method for Solving Three-Dimensional Elliptic Interface Problems","authors":"Kumudu Gamage,Yan Peng, Zhilin Li","doi":"10.4208/ijnam2024-1014","DOIUrl":"https://doi.org/10.4208/ijnam2024-1014","url":null,"abstract":"This paper presents a direct method for efficiently solving three-dimensional elliptic\u0000interface problems featuring piecewise constant coefficients with a finite jump across the interface.\u0000A key advantage of our approach lies in its avoidance of augmented variables, distinguishing\u0000it from traditional methods. The computational framework relies on a finite difference scheme\u0000implemented on a uniform Cartesian grid system. By utilizing a seven-point Laplacian for grid\u0000points away from the interface, our method only requires coefficient modifications for grid points\u0000located near or on the interface. Numerical experiments validate our method’s effectiveness.\u0000Generally, it achieves second-order accuracy for both the solution and its gradient, measured in\u0000the maximum norm, particularly effective in scenarios with moderate coefficient jumps. Extending\u0000and building upon the recent work of [1] on 1D and 2D elliptic interfaces, our approach successfully\u0000introduces a simpler method for extension into three dimensions. Notably, our proposed method\u0000not only offers efficiency and accuracy but also enhances the simplicity of implementation, making\u0000it accessible to non-experts in the field.","PeriodicalId":50301,"journal":{"name":"International Journal of Numerical Analysis and Modeling","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Fast Numerical Solvers for Subdiffusion Problems with Spatial Interfaces 空间界面亚扩散问题的快速数值求解器

IF 1.1 4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2024-05-01 DOI: 10.4208/ijnam2024-1017

Boyang Yu,Yonghai Li, Jiangguo Liu

引用次数: 0

CFIRM: An Integrated Code Package for the Low-Temperature Plasma Simulation on Structured Grids CFIRM：结构网格低温等离子体模拟集成代码包

IF 1.1 4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2024-05-01 DOI: 10.4208/ijnam2024-1015

Jinwei Bai,Hongtao Liu,Xiaoming He,Wei Jiang, Yong Cao

{"title":"CFIRM: An Integrated Code Package for the Low-Temperature Plasma Simulation on Structured Grids","authors":"Jinwei Bai,Hongtao Liu,Xiaoming He,Wei Jiang, Yong Cao","doi":"10.4208/ijnam2024-1015","DOIUrl":"https://doi.org/10.4208/ijnam2024-1015","url":null,"abstract":"This paper presents a recently developed full kinetic particle simulation code package, which is a two-dimensional highly integrated and universal framework for low-temperature\u0000plasma simulation on both Cartesian and axisymmetric coordinate systems. This code package\u0000is named CFIRM, since it is designed based on the continuous Galerkin immersed-finite-element\u0000(IFE) particle-in-cell (PIC) model with the polynomial-preserving-recovery (PPR) technique and\u0000the Monte-Carlo-collision (MCC) method. Both the traditional and implicit PIC methods were\u0000implemented in the package. Incorporating the advantages of all these methods together, the\u0000CFIRM code can adopt explicit or implicit PIC schemes to track the motion trajectory of charged\u0000particles and deal with the collisions between plasma and neutral gas. Additionally, it can conveniently handle complex interface problems on structured grids. The CFRIM code has excellent\u0000versatility in low-temperature plasma simulation and can easily extend to various particle processing modules, such as the variable weights and adaptive particle management algorithms which\u0000were incorporated into this code to reduce the memory utilization rate. The implementation for\u0000the main algorithms and the overall simulation framework of the CFIRM code package are rigorously described in details. Several simulations of the benchmark cases are carried out to validate\u0000the reliability and accuracy of the CFIRM code. Moreover, two typical low-temperature plasma\u0000engineering problems are simulated, including a hall thruster and a capacitively coupled plasma\u0000reactor, which demonstrates the applicability of this code package.","PeriodicalId":50301,"journal":{"name":"International Journal of Numerical Analysis and Modeling","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Continuous/Discontinuous Finite Element Approximation of a 2d Navier-Stokes Problem Arising in Fluid Confinement 流体封闭中出现的二维 Navier-Stokes 问题的连续/非连续有限元逼近

IF 1.1 4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2024-05-01 DOI: 10.4208/ijnam2024-1013

Hermenegildo Borges De Oliveira, Nuno David Lopes

引用次数: 0