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
Error estimates for full discretization of Cahn–Hilliard equation with dynamic boundary conditions 带动态边界条件的卡恩-希利亚德方程全离散化的误差估计
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2025-04-04 DOI: 10.1093/imanum/draf009
Nils Bullerjahn, Balázs Kovács
{"title":"Error estimates for full discretization of Cahn–Hilliard equation with dynamic boundary conditions","authors":"Nils Bullerjahn, Balázs Kovács","doi":"10.1093/imanum/draf009","DOIUrl":"https://doi.org/10.1093/imanum/draf009","url":null,"abstract":"A proof of optimal-order error estimates is given for the full discretization of the Cahn–Hilliard equation with Cahn–Hilliard-type dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk–surface finite element discretization in space and linearly implicit backward difference formulae of order 1 to 5 in time. Optimal-order error estimates are proven. The error estimates are based on a consistency and stability analysis in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second-order system.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"16 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143782663","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
Optimal distributions for randomized unbiased estimators with an infinite horizon and an adaptive algorithm
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2025-04-03 DOI: 10.1093/imanum/draf017
Chao Zheng, Jiangtao Pan, Qun Wang
{"title":"Optimal distributions for randomized unbiased estimators with an infinite horizon and an adaptive algorithm","authors":"Chao Zheng, Jiangtao Pan, Qun Wang","doi":"10.1093/imanum/draf017","DOIUrl":"https://doi.org/10.1093/imanum/draf017","url":null,"abstract":"The randomized unbiased estimators of Rhee & Glynn (2015, Unbiased estimation with square root convergence for SDE models. Oper. Res, 63, 1026–1043) can be highly efficient at approximating expectations of path functionals associated with stochastic differential equations. However, algorithms for calculating the optimal distributions with an infinite horizon are lacking. In this article, based on the method of Cui et al. (2021, On the optimal design of the randomized unbiased Monte Carlo estimators. Oper. Res. Lett., 49, 477–484), we prove that, under mild assumptions, there is a simple representation of the optimal distributions. Then, we develop an adaptive algorithm to compute the optimal distributions with an infinite horizon, which requires only a small amount of computational time in prior estimation. Finally, we provide numerical results to illustrate the efficiency of our adaptive algorithm.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"73 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143775386","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
Energy stable semi-implicit schemes for the 2D Allen–Cahn and fractional Cahn–Hilliard equations
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2025-03-31 DOI: 10.1093/imanum/draf010
Xinyu Cheng
{"title":"Energy stable semi-implicit schemes for the 2D Allen–Cahn and fractional Cahn–Hilliard equations","authors":"Xinyu Cheng","doi":"10.1093/imanum/draf010","DOIUrl":"https://doi.org/10.1093/imanum/draf010","url":null,"abstract":"In this work, we are interested in a class of numerical schemes for certain phase field models. It is well known that unconditional energy stability (energy decays in time regardless of the size of the time step) provides a fidelity check in practical numerical simulations. In recent work (Li, D. (2022b, Why large time-stepping methods for the Cahn–Hilliard equation is stable. Math. Comp., 91, 2501–2515)), a type of semi-implicit scheme for the Cahn–Hilliard (CH) equation with regular potential was developed satisfying the energy-decay property. In this paper, we extend such semi-implicit schemes to the Allen–Cahn equation and the fractional CH equation with a rigorous proof of similar energy stability. Models in two spatial dimensions are discussed.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"72 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143744936","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
Optimal convergence of the arbitrary Lagrangian–Eulerian interface tracking method for two-phase Navier–Stokes flow without surface tension
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2025-03-29 DOI: 10.1093/imanum/draf003
Buyang Li, Shu Ma, Weifeng Qiu
{"title":"Optimal convergence of the arbitrary Lagrangian–Eulerian interface tracking method for two-phase Navier–Stokes flow without surface tension","authors":"Buyang Li, Shu Ma, Weifeng Qiu","doi":"10.1093/imanum/draf003","DOIUrl":"https://doi.org/10.1093/imanum/draf003","url":null,"abstract":"Optimal-order convergence in the $H^{1}$ norm is proved for an arbitrary Lagrangian–Eulerian (ALE) interface tracking finite element method (FEM) for the sharp interface model of two-phase Navier–Stokes flow without surface tension, using high-order curved evolving mesh. In this method, the interfacial mesh points move with the fluid’s velocity to track the sharp interface between two phases of the fluid, and the interior mesh points move according to a harmonic extension of the interface velocity. The error of the semidiscrete ALE interface tracking FEM is shown to be $O(h^{k})$ in the $L^infty (0, T; H^{1}(varOmega ))$ norm for the Taylor–Hood finite elements of degree $k geqslant 2$. This high-order convergence is achieved by utilizing the piecewise smoothness of the solution on each subdomain occupied by one phase of the fluid, relying on a low global regularity on the entire moving domain. Numerical experiments illustrate and complement the theoretical results.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143736499","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
Finite element approximation of the Einstein tensor
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
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
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
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
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
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：481959085
Book学术官方微信