发布求助
文献互助 智能选刊 最新文献

IMA Journal of Numerical Analysis最新文献

筛选
英文 中文
Finite element approximation of the Einstein tensor 爱因斯坦张量的有限元近似
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2025-03-29 DOI: 10.1093/imanum/draf004
Evan S Gawlik, Michael Neunteufel
{"title":"Finite element approximation of the Einstein tensor","authors":"Evan S Gawlik, Michael Neunteufel","doi":"10.1093/imanum/draf004","DOIUrl":"https://doi.org/10.1093/imanum/draf004","url":null,"abstract":"We construct and analyse finite element approximations of the Einstein tensor in dimension $N ge 3$. We focus on the setting where a smooth Riemannian metric tensor $g$ on a polyhedral domain $varOmega subset mathbb{R}^{N}$ has been approximated by a piecewise polynomial metric $g_{h}$ on a simplicial triangulation $mathcal{T}$ of $varOmega $ having maximum element diameter $h$. We assume that $g_{h}$ possesses single-valued tangential–tangential components on every codimension-$1$ simplex in $mathcal{T}$. Such a metric is not classically differentiable in general, but it turns out that one can still attribute meaning to its Einstein curvature in a distributional sense. We study the convergence of the distributional Einstein curvature of $g_{h}$ to the Einstein curvature of $g$ under refinement of the triangulation. We show that in the $H^{-2}(varOmega )$-norm this convergence takes place at a rate of $O(h^{r+1})$ when $g_{h}$ is an optimal-order interpolant of $g$ that is piecewise polynomial of degree $r ge 1$. We provide numerical evidence to support this claim. In the process of proving our convergence results we derive a few formulas for the evolution of certain geometric quantities under deformations of the metric.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"72 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143736497","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
Complex generalized Gauss–Radau quadrature rules for Hankel transforms of integer order 整数阶Hankel变换的复广义Gauss-Radau正交规则
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2025-03-23 DOI: 10.1093/imanum/draf007
Haiyong Wang, Menghan Wu
{"title":"Complex generalized Gauss–Radau quadrature rules for Hankel transforms of integer order","authors":"Haiyong Wang, Menghan Wu","doi":"10.1093/imanum/draf007","DOIUrl":"https://doi.org/10.1093/imanum/draf007","url":null,"abstract":"Complex Gaussian quadrature rules for oscillatory integral transforms have the advantage that they can achieve optimal asymptotic order. However, their existence for Hankel transform can only be guaranteed when the order of the transform belongs to $[0,1/2]$. In this paper we introduce a new family of Gaussian quadrature rules for Hankel transforms of integer order. We show that, if adding certain value and derivative information at the left endpoint, then complex generalized Gauss–Radau quadrature rules that guarantee existence can be constructed and their nodes and weights can be calculated from a half-size Gaussian quadrature rule with respect to the generalized Prudnikov weight function. Orthogonal polynomials that are closely related to such quadrature rules are investigated and their existence for even degrees is proved. Numerical experiments are presented to show the performance of the proposed rules.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"61 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143677760","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 schemes for radial Dunkl processes 径向Dunkl过程的数值格式
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2025-03-12 DOI: 10.1093/imanum/draf005
Hoang-Long Ngo, Dai Taguchi
{"title":"Numerical schemes for radial Dunkl processes","authors":"Hoang-Long Ngo, Dai Taguchi","doi":"10.1093/imanum/draf005","DOIUrl":"https://doi.org/10.1093/imanum/draf005","url":null,"abstract":"We consider the numerical approximation for a class of radial Dunkl processes corresponding to arbitrary (reduced) root systems in $mathbb{R}^{d}$. This class contains well-known processes such as Bessel processes, Dyson’s Brownian motions and square root of Wishart processes. We propose some semi-implicit and truncated Euler–Maruyama schemes for radial Dunkl processes and study their convergence rate with respect to the $L^{p}$-sup norm.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"21 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143607954","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 systems of hyperbolic conservation laws via computing negative norms of local residuals 计算局部残差负规范的双曲守恒律系统的后验误差估计
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2025-03-11 DOI: 10.1093/imanum/drae111
Jan Giesselmann, Aleksey Sikstel
{"title":"A-posteriori error estimates for systems of hyperbolic conservation laws via computing negative norms of local residuals","authors":"Jan Giesselmann, Aleksey Sikstel","doi":"10.1093/imanum/drae111","DOIUrl":"https://doi.org/10.1093/imanum/drae111","url":null,"abstract":"We prove rigorous a-posteriori error estimates for first-order finite-volume approximations of nonlinear systems of hyperbolic conservation laws in one spatial dimension. Our estimators rely on recent stability results by Bressan, Chiri and Shen, a new way to localize residuals and a novel method to compute negative-order norms of these local residuals. Computing negative-order norms becomes possible by suitably projecting test functions onto a finite dimensional space. Numerical experiments show that the error estimator converges with the rate predicted by a-priori error estimates.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"10 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143599894","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
Well-posedness of first-order acoustic wave equations and space-time finite element approximation 一阶声波方程的良好拟合与时空有限元近似
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2025-03-11 DOI: 10.1093/imanum/drae104
Thomas Führer, Roberto González, Michael Karkulik
{"title":"Well-posedness of first-order acoustic wave equations and space-time finite element approximation","authors":"Thomas Führer, Roberto González, Michael Karkulik","doi":"10.1093/imanum/drae104","DOIUrl":"https://doi.org/10.1093/imanum/drae104","url":null,"abstract":"We study a first-order system formulation of the (acoustic) wave equation and prove that the operator of this system is an isomorphism from an appropriately defined graph space to $L^{2}$. The results rely on well-posedness and stability of the weak and ultraweak formulation of the second-order wave equation. As an application, we define and analyze a space-time least-squares finite element method for solving the wave equation. Some numerical examples for one- and two-dimensional spatial domains are presented.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"86 1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143599893","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 noncoforming virtual element approximation for the Oseen eigenvalue problem Oseen特征值问题的非共形虚元逼近
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2025-03-11 DOI: 10.1093/imanum/drae108
Dibyendu Adak, Felipe Lepe, Gonzalo Rivera
{"title":"A noncoforming virtual element approximation for the Oseen eigenvalue problem","authors":"Dibyendu Adak, Felipe Lepe, Gonzalo Rivera","doi":"10.1093/imanum/drae108","DOIUrl":"https://doi.org/10.1093/imanum/drae108","url":null,"abstract":"In this paper, we analyze a nonconforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. The spaces under consideration lead to a divergence-free method that is capable to capture properly the divergence at discrete level and the eigenvalues and eigenfunctions. Under the compact theory for operators, we prove convergence and error estimates for the method. By employing the theory of compact operators, we recover the double order of convergence of the spectrum. Finally, we present numerical tests to assess the performance of the proposed numerical scheme.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"12 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143599895","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
Geometry error analysis of a parametric mapping for higher order unfitted space–time methods 高阶非拟合时空方法参数映射的几何误差分析
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2025-03-10 DOI: 10.1093/imanum/drae098
Fabian Heimann, Christoph Lehrenfeld
{"title":"Geometry error analysis of a parametric mapping for higher order unfitted space–time methods","authors":"Fabian Heimann, Christoph Lehrenfeld","doi":"10.1093/imanum/drae098","DOIUrl":"https://doi.org/10.1093/imanum/drae098","url":null,"abstract":"In Heimann, Lehrenfeld, and Preuß (2023, SIAM J. Sci. Comp., 45(2), B139–B165), new geometrically unfitted space–time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and time have been introduced. For geometrically higher-order accuracy a parametric mapping on a background space–time tensor-product mesh has been used. In this paper, we concentrate on the geometrical accuracy of the approximation and derive rigorous bounds for the distance between the realized and an ideal mapping in different norms and derive results for the space–time regularity of the parametric mapping. These results are important and lay the ground for the error analysis of corresponding unfitted space–time finite element methods.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"17 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143599897","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
Analysis and finite element approximation of a diffuse interface approach to the Stokes–Biot coupling Stokes-Biot耦合扩散界面方法的分析与有限元逼近
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2025-03-10 DOI: 10.1093/imanum/draf002
Francis R A Aznaran, Martina Bukač, Boris Muha, Abner J Salgado
{"title":"Analysis and finite element approximation of a diffuse interface approach to the Stokes–Biot coupling","authors":"Francis R A Aznaran, Martina Bukač, Boris Muha, Abner J Salgado","doi":"10.1093/imanum/draf002","DOIUrl":"https://doi.org/10.1093/imanum/draf002","url":null,"abstract":"We consider the interaction between a poroelastic structure, described using the Biot model in primal form, and a free-flowing fluid, modelled with the time-dependent incompressible Stokes equations. We propose a diffuse interface model in which a phase field function is used to write each integral in the weak formulation of the coupled problem on the entire domain containing both the Stokes and Biot regions. The phase field function continuously transitions from one to zero over a diffuse region of width $mathcal{O}(varepsilon)$ around the interface; this allows the weak forms to be integrated uniformly across the domain, and obviates tracking the subdomains or the interface between them. We prove convergence in weighted norms of a finite element discretization of the diffuse interface model to the continuous diffuse model; here the weight is a power of the distance to the diffuse interface. We, in turn, prove convergence of the continuous diffuse model to the standard, sharp interface, model. Numerical examples verify the proven error estimates, and illustrate application of the method to fluid flow through a complex network, describing blood circulation in the circle of Willis.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"54 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143599896","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
Tensorized block rational Krylov methods for tensor Sylvester equations 张量Sylvester方程的张张化块有理Krylov方法
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2025-03-05 DOI: 10.1093/imanum/draf001
Angelo A Casulli
{"title":"Tensorized block rational Krylov methods for tensor Sylvester equations","authors":"Angelo A Casulli","doi":"10.1093/imanum/draf001","DOIUrl":"https://doi.org/10.1093/imanum/draf001","url":null,"abstract":"We introduce the definition of tensorized block rational Krylov subspace and its relation with multivariate rational functions, extending the formulation of tensorized Krylov subspaces introduced in Kressner, D. & Tobler, C. (2010) Krylov subspace methods for linear systems with tensor product structure. SIAM J. Matrix Anal. Appl., 31,$1688$–$1714$. Moreover, we develop methods for the solution of tensor Sylvester equations with low multilinear or tensor train rank, based on projection onto a tensor block rational Krylov subspace. We provide a convergence analysis, some strategies for pole selection and techniques to efficiently compute the residual.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"10 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143546177","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
Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods 非连续最小二乘有限元方法的尺度鲁棒后验误差估计
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2025-03-05 DOI: 10.1093/imanum/drae105
Philipp Bringmann
{"title":"Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods","authors":"Philipp Bringmann","doi":"10.1093/imanum/drae105","DOIUrl":"https://doi.org/10.1093/imanum/drae105","url":null,"abstract":"A convincing feature of least-squares finite element methods is the built-in a posteriori error estimator for any conforming discretization. In order to generalize this property to discontinuous finite element ansatz functions, this paper introduces a least-squares principle on piecewise Sobolev functions by the example of the Poisson model problem with mixed boundary conditions. It allows for fairly general discretizations including standard piecewise polynomial ansatz spaces on triangular and polygonal meshes. The presented scheme enforces the interelement continuity of the piecewise polynomials by additional least-squares residuals. A side condition on the normal jumps of the flux variable requires a vanishing integral mean and enables the penalization of the jump with the natural power of the mesh size in the least-squares functional. This avoids over-penalization with additional regularity assumptions on the exact solution as usually present in the literature on discontinuous LSFEM. The proof of the built-in a posteriori error estimation for the over-penalized scheme is presented as well. All results in this paper are robust with respect to the size of the domain guaranteed by a suitable weighting of the residuals in the least-squares functional. Numerical experiments illustrate the importance of the proposed weighting and exhibit optimal convergence rates of the adaptive mesh-refining algorithm for various polynomial degrees.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"35 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143546180","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信