International Journal of Numerical Analysis and Modeling最新文献_第2页

A Fully Implicit Method Using Nodal Radial Basis Functions to Solve the Linear Advection Equation 利用节点径向基函数求解线性平流方程的全隐式方法

4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2023-06-01 DOI: 10.4208/ijnam2023-1018

P.-A. Gourdain, M. Evans, H. R. Hasson, J. R. Young, I. West-Abdallah null, M. B. Adams

引用次数: 0

Improved Long Time Accuracy for Projection Methods for Navier-Stokes Equations Using Emac Formulation 利用Emac公式提高Navier-Stokes方程投影方法的长时间精度

4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2023-06-01 DOI: 10.4208/ijnam2023-1008

Sean Ingimarson, Monika Neda, Leo G. Rebholz, Jorge Reyes null, An Vu

引用次数: 1

A Sharp $alpha$-Robust $L1$ Scheme on Graded Meshes for Two-Dimensional Time Tempered Fractional Fokker-Planck Equation 二维时间调质分数阶Fokker-Planck方程梯度网格上的Sharp $alpha$-Robust $L1$格式

4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2023-06-01 DOI: 10.4208/ijnam2023-1033

Can Wang, Weihua Deng null, Xiangong Tang

引用次数: 0

A Posteriori Error Estimates for a Local Discontinuous Galerkin Approximation of Semilinear Second-Order Elliptic Problems on Cartesian Grids 直角网格上半线性二阶椭圆问题局部不连续Galerkin逼近的后验误差估计

4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2023-06-01 DOI: 10.4208/ijnam2023-1034

Mahboub Baccouch

{"title":"A Posteriori Error Estimates for a Local Discontinuous Galerkin Approximation of Semilinear Second-Order Elliptic Problems on Cartesian Grids","authors":"Mahboub Baccouch","doi":"10.4208/ijnam2023-1034","DOIUrl":"https://doi.org/10.4208/ijnam2023-1034","url":null,"abstract":". In this paper, we design and analyze new residual-type a posteriori error estimators for the local discontinuous Galerkin (LDG) method applied to semilinear second-order elliptic problems in two dimensions of the type (cid:0) ∆ u = f ( x ;u ). We use our recent superconvergence results derived in Commun. Appl. Math. Comput. (2021) to prove that the LDG solution is superconvergent with an order p +2 towards the p -degree right Radau interpolating polynomial of the exact solution, when tensor product polynomials of degree at most p are considered as basis for the LDG method. Moreover, we show that the global discretization error can be decomposed into the sum of two errors. The ﬁrst error can be expressed as a linear combination of two ( p +1)- degree Radau polynomials in the x - and y (cid:0) directions. The second error converges to zero with order p + 2 in the L 2 -norm. This new result allows us to construct a posteriori error estimators of residual type. We prove that the proposed a posteriori error estimators converge to the true errors in the L 2 -norm under mesh reﬁnement at the optimal rate. The order of convergence is proved to be p + 2. We further prove that our a posteriori error estimates yield upper and lower bounds for the actual error. Finally, a series of numerical examples are presented to validate the theoretical results and numerically demonstrate the convergence of the proposed a posteriori error estimators.","PeriodicalId":50301,"journal":{"name":"International Journal of Numerical Analysis and Modeling","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135195303","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 Finite Volume Element Solution Based on Postprocessing Technique Over Arbitrary Convex Polygonal Meshes 基于后处理技术的任意凸多边形网格有限体积元解

4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2023-06-01 DOI: 10.4208/ijnam2023-1026

Yanlong Zhang null, Yanhui Zhou

{"title":"A Finite Volume Element Solution Based on Postprocessing Technique Over Arbitrary Convex Polygonal Meshes","authors":"Yanlong Zhang null, Yanhui Zhou","doi":"10.4208/ijnam2023-1026","DOIUrl":"https://doi.org/10.4208/ijnam2023-1026","url":null,"abstract":". A special (cid:12)nite volume element method based on postprocessing technique is proposed to solve the anisotropic di(cid:11)usion problem on arbitrary convex polygonal meshes. The shape function of polygonal (cid:12)nite element method is constructed by Wachspress generalized barycentric coordinate, and by adding some element-wise bubble functions to the (cid:12)nite element solution, we get a new (cid:12)nite volume element solution that satis(cid:12)es the local conservation law on a certain dual mesh. The postprocessing algorithm only needs to solve a local linear algebraic system on each primary cell, so that it is easy to implement. More interesting is that, a general construction of the bubble functions is introduced on each polygonal cell, which enables us to prove the existence and uniqueness of the post-processed solution on arbitrary convex polygonal meshes with full anisotropic di(cid:11)usion tensor. The optimal H 1 and L 2 error estimates of the post-processed solution are also obtained. Finally, the local conservation property and convergence of the new polygonal (cid:12)nite volume element solution are veri(cid:12)ed by numerical experiments.","PeriodicalId":50301,"journal":{"name":"International Journal of Numerical Analysis and Modeling","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135143757","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

Fractional Order Learning Methods for Nonlinear System Identification Based on Fuzzy Neural Network 基于模糊神经网络的非线性系统辨识分数阶学习方法

4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2023-06-01 DOI: 10.4208/ijnam2023-1031

Jie Ding, Sen Xu null, Zhijie Li

引用次数: 0

Newton-Anderson at Singular Points 牛顿-安德森奇异点定理

4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2023-06-01 DOI: 10.4208/ijnam2023-1029

Matt Dallas null, Sara Pollock

引用次数: 0

Orthogonal Spline Collocation for Poisson’S Equation with Neumann Boundary Conditions 具有Neumann边界条件的Poisson方程的正交样条配置

4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2023-06-01 DOI: 10.4208/ijnam2023-1036

Bernard Bialecki null, Nick Fisher

引用次数: 0

A New Weak Galerkin Method with Weakly Enforced Dirichlet Boundary Condition 具有弱强制Dirichlet边界条件的弱Galerkin方法

4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2023-06-01 DOI: 10.4208/ijnam2023-1028

Dan Li, Yiqiang Li null, Zhanbin Yuan

引用次数: 0

A Posteriori Error Analysis for an Ultra-Weak Discontinuous Galerkin Approximations of Nonlinear Second-Order Two-Point Boundary-Value Problems 非线性二阶两点边值问题的超弱不连续Galerkin逼近的后验误差分析

4区数学

International Journal of Numerical Analysis and Modeling Pub Date : 2023-06-01 DOI: 10.4208/ijnam2023-1027

Mahboub Baccouch

{"title":"A Posteriori Error Analysis for an Ultra-Weak Discontinuous Galerkin Approximations of Nonlinear Second-Order Two-Point Boundary-Value Problems","authors":"Mahboub Baccouch","doi":"10.4208/ijnam2023-1027","DOIUrl":"https://doi.org/10.4208/ijnam2023-1027","url":null,"abstract":". In this paper, we present and analyze a posteriori error estimates in the L 2 -norm of an ultra-weak discontinuous Galerkin (UWDG) method for nonlinear second-order boundary-value problems for ordinary di(cid:11)erential equations of the form u ′′ = f ( x;u ). We (cid:12)rst use the superconvergence results proved in the (cid:12)rst part of this paper ( J. Appl. Math. Comput. 69, 1507-1539, 2023) to prove that the UWDG solution converges, in the L 2 -norm, towards a special p -degree interpolating polynomial, when piecewise polynomials of degree at most p (cid:21) 2 are used. The order of convergence is proved to be p + 2. We then show that the UWDG error on each element can be divided into two parts. The dominant part is proportional to a special ( p +1)-degree Baccouch polynomial, which can be written as a linear combination of Legendre polynomials of degrees p (cid:0) 1, p , and p + 1. The second part converges to zero with order p + 2 in the L 2 - norm. These results allow us to construct a posteriori UWDG error estimates. The proposed error estimates are computationally simple and are obtained by solving a local problem with no boundary conditions on each element. Furthermore, we prove that, for smooth solutions, these a posteriori error estimates converge to the exact errors in the L 2 -norm under mesh re(cid:12)nement. The order of convergence is proved to be p + 2. Finally, we prove that the global e(cid:11)ectivity index converges to unity at O ( h ) rate. Numerical results are presented exhibiting the reliability and the e(cid:14)ciency of the proposed error estimator.","PeriodicalId":50301,"journal":{"name":"International Journal of Numerical Analysis and Modeling","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135143756","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