IMA Journal of Numerical Analysis最新文献_第8页

Compactness estimates for difference schemes for conservation laws with discontinuous flux 非连续通量守恒定律差分方案的紧凑性估计

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2024-01-04 DOI: 10.1093/imanum/drad096

Kenneth H Karlsen, John D Towers

引用次数: 0

A constraint dissolving approach for nonsmooth optimization over the Stiefel manifold 在 Stiefel 流形上进行非平滑优化的约束消解方法

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2023-12-23 DOI: 10.1093/imanum/drad098

Xiaoyin Hu, Nachuan Xiao, Xin Liu, Kim-Chuan Toh

{"title":"A constraint dissolving approach for nonsmooth optimization over the Stiefel manifold","authors":"Xiaoyin Hu, Nachuan Xiao, Xin Liu, Kim-Chuan Toh","doi":"10.1093/imanum/drad098","DOIUrl":"https://doi.org/10.1093/imanum/drad098","url":null,"abstract":"This paper focuses on the minimization of a possibly nonsmooth objective function over the Stiefel manifold. The existing approaches either lack efficiency or can only tackle prox-friendly objective functions. We propose a constraint dissolving function named NCDF and show that it has the same first-order stationary points and local minimizers as the original problem in a neighborhood of the Stiefel manifold. Furthermore, we show that the Clarke subdifferential of NCDF is easy to achieve from the Clarke subdifferential of the objective function. Therefore, various existing approaches for unconstrained nonsmooth optimization can be directly applied to nonsmooth optimization problems over the Stiefel manifold. We propose a framework for developing subgradient-based methods and establishing their convergence properties based on prior works. Furthermore, based on our proposed framework, we can develop efficient approaches for optimization over the Stiefel manifold. Preliminary numerical experiments further highlight that the proposed constraint dissolving approach yields efficient and direct implementations of various unconstrained approaches to nonsmooth optimization problems over the Stiefel manifold.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"87 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139041468","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

On best p-norm approximation of discrete data by polynomials 论多项式对离散数据的最佳 p-norm 近似值

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2023-12-09 DOI: 10.1093/imanum/drad086

Michael S Floater

引用次数: 0

Semilinear optimal control with Dirac measures 具有狄拉克测度的半线性最优控制

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2023-11-29 DOI: 10.1093/imanum/drad091

Enrique Otárola

引用次数: 3

Unconditionally stable small stencil enriched multiple point flux approximations of heterogeneous diffusion problems on general meshes 一般网格上非均匀扩散问题的无条件稳定小模板富多点通量近似

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2023-11-25 DOI: 10.1093/imanum/drad087

Julien Coatléven

引用次数: 0

Adaptive VEM for variable data: convergence and optimality 可变数据的自适应VEM:收敛性和最优性

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2023-11-16 DOI: 10.1093/imanum/drad085

L Beirão da Veiga, C Canuto, R H Nochetto, G Vacca, M Verani

{"title":"Adaptive VEM for variable data: convergence and optimality","authors":"L Beirão da Veiga, C Canuto, R H Nochetto, G Vacca, M Verani","doi":"10.1093/imanum/drad085","DOIUrl":"https://doi.org/10.1093/imanum/drad085","url":null,"abstract":"We design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilization-free a posteriori error estimators recently derived in Beirão da Veiga et al. (2023, Adaptive VEM: stabilization-free a posteriori error analysis and contraction property. SIAM J. Numer. Anal., 61, 457–494). The crucial property, which also plays a central role in this paper, is that the stabilization term can be made arbitrarily small relative to the a posteriori error estimators upon increasing the stabilization parameter. Our AVEM concatenates two modules, GALERKIN and DATA. The former deals with piecewise constant data and is shown in the above article to be a contraction between consecutive iterates. The latter approximates general data by piecewise constants to a desired accuracy. AVEM is shown to be convergent and quasi-optimal, in terms of error decay versus degrees of freedom, for solutions and data belonging to appropriate approximation classes. Numerical experiments illustrate the interplay between these two modules and provide computational evidence of optimality.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"5 5","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138293500","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 two-dimensional boundary value problem of elliptic type with nonlocal conjugation conditions 具有非局部共轭条件的椭圆型二维边值问题

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2023-11-14 DOI: 10.1093/imanum/drad084

Zorica Milovanović Jeknić, Aleksandra Delić, Sandra Živanović

引用次数: 0

Convergent finite element methods for the perfect conductivity problem with close-to-touching inclusions 近接触夹杂物完美电导率问题的收敛有限元方法

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2023-11-14 DOI: 10.1093/imanum/drad088

Buyang Li, Haigang Li, Zongze Yang

{"title":"Convergent finite element methods for the perfect conductivity problem with close-to-touching inclusions","authors":"Buyang Li, Haigang Li, Zongze Yang","doi":"10.1093/imanum/drad088","DOIUrl":"https://doi.org/10.1093/imanum/drad088","url":null,"abstract":"In the perfect conductivity problem (i.e., the conductivity problem with perfectly conducting inclusions), the gradient of the electric field is often very large in a narrow region between two inclusions and blows up as the distance between the inclusions tends to zero. The rigorous error analysis for the computation of such perfect conductivity problems with close-to-touching inclusions of general geometry still remains open in three dimensions. We address this problem by establishing new asymptotic estimates for the second-order partial derivatives of the solution with explicit dependence on the distance $varepsilon $ between the inclusions, and use the asymptotic estimates to design a class of graded meshes and finite element spaces to solve the perfect conductivity problem with possibly close-to-touching inclusions. In particular, we propose a special finite element basis function that resolves the asymptotic singularity of the solution by making the interpolation error bounded in $W^{1,infty }$ in a neighborhood of the close-to-touching point, even though the solution itself is blowing up in $W^{1,infty }$. This is crucial in the error analysis for the numerical approximations. We prove that the proposed method yields optimal-order convergence in the $H^1$ norm, uniformly with respect to the distance $varepsilon $ between the inclusions, in both two and three dimensions for general convex smooth inclusions, which are possibly close-to-touching. Numerical experiments are presented to support the theoretical analysis and to illustrate the convergence of the proposed method for different shapes of inclusions in both two- and three-dimensional domains.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"27 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"109126945","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

Weak error analysis for strong approximation schemes of SDEs with super-linear coefficients 超线性系数SDEs强逼近格式的弱误差分析

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2023-11-11 DOI: 10.1093/imanum/drad083

Xiaojie Wang, Yuying Zhao, Zhongqiang Zhang

引用次数: 2

Numerical analysis of a hybridized discontinuous Galerkin method for the Cahn–Hilliard problem Cahn-Hilliard问题的杂化不连续Galerkin方法的数值分析

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2023-11-11 DOI: 10.1093/imanum/drad075

Keegan L A Kirk, Beatrice Riviere, Rami Masri

引用次数: 0