SIAM Journal on Numerical Analysis最新文献_第3页

Robust Stability and Preconditioning of Darcy–Forchheimer Equations Darcy-Forchheimer方程的鲁棒稳定性与预处理

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-08-11 DOI: 10.1137/25m1816115

Rishi Das, Harsha Hutridurga, Amiya K. Pani, Ricardo Ruiz-Baier

引用次数: 0

Theory and Internal Structure of ADER-DG Method for Ordinary Differential Equations 常微分方程的ADER-DG方法的理论和内部结构

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-08-06 DOI: 10.1137/25m1787008

Ivan S. Popov

引用次数: 0

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs 利用非对称类kansa方法求解偏微分方程，扩展数据以提高稳定性和误差估计

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-08-05 DOI: 10.1137/25m1777724

Thomas Hangelbroek, Francis J. Narcowich, Joesph D. Ward

{"title":"Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs","authors":"Thomas Hangelbroek, Francis J. Narcowich, Joesph D. Ward","doi":"10.1137/25m1777724","DOIUrl":"https://doi.org/10.1137/25m1777724","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 4, Page 1539-1560, August 2026. <br/> Abstract. In this paper, a theoretical framework is presented for the use of a Kansa-like method to numerically solve elliptic partial differential equations on spheres and other manifolds. The theory addresses both the stability of the method and provides error estimates for two different approximation methods. A Kansa-like matrix is obtained by replacing the test point set [math], used in the traditional Kansa method, with a larger set [math], which is a norming set for the underlying trial space. This gives rise to a rectangular matrix. In addition, if a suitable basis is used for the trial space, then it is shown that the stability of the matrix is comparable to the stability of the elliptic operator acting on the trial space. Finally, two different types of error estimates are given. Discrete least squares estimates of very high accuracy are obtained for solutions that are sufficiently smooth. The second method, giving similar error estimates, uses a rank revealing factorization to create a “thinning algorithm” that reduces [math] to [math]. In practice, this algorithm doesn’t need [math] to be a norming set. Finally, throughout the paper, we illustrate our results by focusing on a concrete example: for problems on spheres we consider Kansa matrices constructed with the basis of Lagrange functions for thin-plate spline kernels.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"26 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148674998","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

Computing Rough Solutions of the KdV Equation Below [math] 下面KdV方程的粗解计算[数学]

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-08-04 DOI: 10.1137/25m176177x

Jiachuan Cao, Buyang Li, Yifei Wu, Fangyan Yao

引用次数: 0

Sobolev–Poincaré Inequalities for Piecewise [math][math] Functions over General Polytopic Meshes 一般多边形网格上分段函数的sobolev - poincar<e:1>不等式

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-07-31 DOI: 10.1137/25m1748470

Michele Botti, Lorenzo Mascotto

引用次数: 0

Localized Estimation of Condition Numbers for MILU Preconditioners on a Graph 图上MILU预调节器条件数的局部估计

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-07-30 DOI: 10.1137/24m1722134

Geonho Hwang, Yesom Park, Yueun Lee, Jooyoung Hahn, Myungjoo Kang

{"title":"Localized Estimation of Condition Numbers for MILU Preconditioners on a Graph","authors":"Geonho Hwang, Yesom Park, Yueun Lee, Jooyoung Hahn, Myungjoo Kang","doi":"10.1137/24m1722134","DOIUrl":"https://doi.org/10.1137/24m1722134","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 4, Page 1443-1477, August 2026. <br/> Abstract. This paper proposes a theoretical framework for analyzing modified incomplete LU (MILU) preconditioners for coefficient matrices that are symmetric positive definite M-matrices. Considering a generalized MILU preconditioner on a weighted undirected graph with self-loops, we extend its applicability beyond matrices derived from Poisson equation solvers on uniform grids with compact stencils. A major contribution is a novel measure, the localized estimator of condition number (LECN), which quantifies the condition number locally at each vertex of the graph. We prove that the maximum value of the LECN provides an upper bound for the condition number of the MILU-preconditioned system, offering an estimation of the condition number using only local measurements. This localized approach significantly simplifies the condition number estimation and provides a powerful tool for analyzing the MILU preconditioner applied to previously unexplored matrix structures. To demonstrate the usability of LECN analysis, we present three cases: (1) a revisit of existing results of MILU preconditioners on uniform grids, (2) analysis of high-order implicit finite difference schemes on wide stencils, and (3) analysis of variable coefficient Poisson equations on hierarchical adaptive grids such as quadtree and octree. For the third case, we also validate LECN analysis numerically on a quadtree.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"47 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148624292","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

Convergence Analysis of SPH Method on Irregular Particle Distributions for the Poisson Equation 泊松方程不规则粒子分布SPH方法的收敛性分析

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-07-23 DOI: 10.1137/24m1720792

Zhonghua Qiao, Yifan Wei

引用次数: 0

[math][math]-Reconstruction of Piecewise Polynomial Fields with Application to [math]-a Posteriori Nonconforming Error Analysis for Maxwell’s Equations [math]-分段多项式域的重构及其在[math]中的应用-麦克斯韦方程组的后验不一致误差分析

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-07-20 DOI: 10.1137/25m1789433

Zhaonan Dong, Alexandre Ern

{"title":"[math][math]-Reconstruction of Piecewise Polynomial Fields with Application to [math]-a Posteriori Nonconforming Error Analysis for Maxwell’s Equations","authors":"Zhaonan Dong, Alexandre Ern","doi":"10.1137/25m1789433","DOIUrl":"https://doi.org/10.1137/25m1789433","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 4, Page 1390-1413, August 2026. <br/> Abstract. We devise and analyze a novel [math]-reconstruction operator for piecewise polynomial fields on shape-regular simplicial meshes. The (nonpolynomial) reconstruction is devised over the mesh vertex patches using the partition of unity induced by hat basis functions in combination with local Helmholtz decompositions. Our main focus is on homogeneous tangential boundary conditions. We prove that the difference between the reconstructed [math]-field and the original, piecewise polynomial field, measured in the broken curl norm and in the [math]-norm, can be bounded in terms of suitable jump norms of the original field. The bounds are always [math]-optimal, and [math]-suboptimal by [math]-order for the broken curl norm and by [math]-order for the [math]-norm. An auxiliary result of independent interest is a novel broken curl, divergence-preserving Poincaré inequality on vertex patches. Moreover, the [math]-norm estimate can be improved to [math]-order suboptimality under a (reasonable) assumption on the uniform elliptic regularity pickup for a Poisson problem with Neumann conditions over the vertex patches. We also discuss extensions of the [math]-reconstruction operator to the prescription of mixed boundary conditions, to agglomerated polytopal meshes, and to convex domains. Finally, we showcase an important application of the [math]-reconstruction operator to the [math]-a posteriori nonconforming error analysis of Maxwell’s equations. We focus on the (symmetric) interior penalty discontinuous Galerkin approximation of some simplified forms of Maxwell’s equations.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"60 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148522491","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

Error Estimates of Time-Splitting Schemes for Nonlinear Klein–Gordon Equation with Rough Data 粗糙数据下非线性Klein-Gordon方程时分裂格式的误差估计

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-07-16 DOI: 10.1137/25m1743296

Lun Ji, Xiaofei Zhao

引用次数: 0

Hierarchical Superlocalized Orthogonal Decomposition Method 层次超定域正交分解法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-07-15 DOI: 10.1137/24m1694458

José C. Garay, Hannah Mohr, Daniel Peterseim, Christoph Zimmer

{"title":"Hierarchical Superlocalized Orthogonal Decomposition Method","authors":"José C. Garay, Hannah Mohr, Daniel Peterseim, Christoph Zimmer","doi":"10.1137/24m1694458","DOIUrl":"https://doi.org/10.1137/24m1694458","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 4, Page 1275-1319, August 2026. <br/> Abstract. We present the construction of a sparse-compressed operator that approximates the solution operator of elliptic PDEs with rough coefficients. To derive the compressed operator, we construct a hierarchical basis of an approximate-solution space, with superlocalized basis functions that are quasi-orthogonal across hierarchy levels with respect to the inner product induced by the energy norm. The superlocalization is achieved through a novel variant of the superlocalized orthogonal decomposition method that is built on corrections of basis functions arising from the localized orthogonal decomposition method. The hierarchical basis not only induces a sparse compression of the solution space but also enables an orthogonal multiresolution decomposition of the approximate-solution operator, decoupling scales and solution contributions of each level of the hierarchy. With this decomposition, the solution of the PDE reduces to the solution of a set of independent linear systems with mesh-independent condition numbers (one system per level) that can be computed simultaneously. We present an accuracy study of the compressed solution operator as well as numerical results illustrating our theoretical findings and beyond, revealing that desired optimal error rates with well-behaved superlocalized basis functions can still be attained even in the challenging case of coefficients with high-contrast channels.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"14 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148441395","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