发布求助
文献互助 智能选刊 最新文献

Journal of Numerical Mathematics最新文献

筛选
英文 中文
A decoupled finite element method with diferent time steps for the nonstationary Darcy-Brinkman problem 非平稳Darcy-Brinkman问题的不同时间步长的解耦有限元方法
IF 3 2区 数学
Journal of Numerical Mathematics Pub Date : 2020-03-26 DOI: 10.1515/JNMA-2018-0080
Liao Cheng, Huang Peng-zhan, He Yinnian
{"title":"A decoupled finite element method with diferent time steps for the nonstationary Darcy-Brinkman problem","authors":"Liao Cheng, Huang Peng-zhan, He Yinnian","doi":"10.1515/JNMA-2018-0080","DOIUrl":"https://doi.org/10.1515/JNMA-2018-0080","url":null,"abstract":"","PeriodicalId":50109,"journal":{"name":"Journal of Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2020-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75378128","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: 4
POD-Galerkin model order reduction for parametrized nonlinear time-dependent optimal flow control: an application to shallow water equations 参数化非线性时变最优流动控制的POD-Galerkin模型降阶:在浅水方程中的应用
IF 3 2区 数学
Journal of Numerical Mathematics Pub Date : 2020-03-21 DOI: 10.1515/jnma-2020-0098
M. Strazzullo, F. Ballarin, G. Rozza
{"title":"POD-Galerkin model order reduction for parametrized nonlinear time-dependent optimal flow control: an application to shallow water equations","authors":"M. Strazzullo, F. Ballarin, G. Rozza","doi":"10.1515/jnma-2020-0098","DOIUrl":"https://doi.org/10.1515/jnma-2020-0098","url":null,"abstract":"Abstract In the present paper we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal with is nonlinear and time dependent: this leads to very time consuming simulations which can be unbearable, e.g., in a marine environmental monitoring plan application. Our aim is to show how reduced order modelling could help in studying different configurations and phenomena in a fast way. After building the optimality system, we rely on a POD-Galerkin reduction in order to solve the optimal control problem in a low dimensional reduced space. The presented theoretical framework is actually suited to general nonlinear time dependent optimal control problems. The proposed methodology is finally tested with a numerical experiment: the reduced optimal control problem governed by shallow waters equations reproduces the desired velocity and height profiles faster than the standard model, still remaining accurate.","PeriodicalId":50109,"journal":{"name":"Journal of Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2020-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73606880","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: 18
Error analysis of higher order Trace Finite Element Methods for the surface Stokes equation 曲面Stokes方程的高阶轨迹有限元法误差分析
IF 3 2区 数学
Journal of Numerical Mathematics Pub Date : 2020-03-16 DOI: 10.1515/jnma-2020-0017
Thomas Jankuhn, M. Olshanskii, A. Reusken, Alexander Zhiliakov
{"title":"Error analysis of higher order Trace Finite Element Methods for the surface Stokes equation","authors":"Thomas Jankuhn, M. Olshanskii, A. Reusken, Alexander Zhiliakov","doi":"10.1515/jnma-2020-0017","DOIUrl":"https://doi.org/10.1515/jnma-2020-0017","url":null,"abstract":"Abstract The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in ℝ3. The method employs parametric Pk-Pk−1 finite element pairs on tetrahedral bulk mesh to discretize the Stokes system on embedded surface. Stability and optimal order convergence results are proved. The proofs include a complete quantification of geometric errors stemming from approximate parametric representation of the surface. Numerical experiments include formal convergence studies and an example of the Kelvin–Helmholtz instability problem on the unit sphere.","PeriodicalId":50109,"journal":{"name":"Journal of Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2020-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84085070","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: 18
On convergent schemes for a two-phase Oldroyd-B type model with variable polymer density 变聚合物密度两相Oldroyd-B型模型的收敛格式
IF 3 2区 数学
Journal of Numerical Mathematics Pub Date : 2019-12-31 DOI: 10.1515/jnma-2019-0019
O. Sieber
{"title":"On convergent schemes for a two-phase Oldroyd-B type model with variable polymer density","authors":"O. Sieber","doi":"10.1515/jnma-2019-0019","DOIUrl":"https://doi.org/10.1515/jnma-2019-0019","url":null,"abstract":"Abstract The paper is concerned with a diffuse-interface model that describes two-phase flow of dilute polymeric solutions with a variable particle density. The additional stresses, which arise by elongations of the polymers caused by deformations of the fluid, are described by Kramers stress tensor. The evolution of Kramers stress tensor is modeled by an Oldroyd-B type equation that is coupled to a Navier–Stokes type equation, a Cahn–Hilliard type equation, and a parabolic equation for the particle density. We present a regularized finite element approximation of this model, prove that our scheme is energy stable and that there exist discrete solutions to it. Furthermore, in the case of equal mass densities and two space dimensions, we are able to pass to the limit rigorously as the regularization parameters and the spatial and temporal discretization parameters tend towards zero and prove that a subsequence of discrete solutions converges to a global-in-time weak solution to the unregularized coupled system. To the best of our knowledge, this is the first existence result for a two-phase flow model of viscoelastic fluids with an Oldroyd-B type equation. Additionally, we show that our finite element scheme is fully practical and we present numerical simulations.","PeriodicalId":50109,"journal":{"name":"Journal of Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75539642","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: 2
Frontmatter
IF 3 2区 数学
Journal of Numerical Mathematics Pub Date : 2019-09-25 DOI: 10.1515/jnma-2019-frontmatter3
{"title":"Frontmatter","authors":"","doi":"10.1515/jnma-2019-frontmatter3","DOIUrl":"https://doi.org/10.1515/jnma-2019-frontmatter3","url":null,"abstract":"","PeriodicalId":50109,"journal":{"name":"Journal of Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2019-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89736826","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
Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems 二阶椭圆型问题的内罚杂交不连续Galerkin方法族
IF 3 2区 数学
Journal of Numerical Mathematics Pub Date : 2019-09-06 DOI: 10.1515/jnma-2019-0027
M. Fabien, M. Knepley, B. Rivière
{"title":"Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems","authors":"M. Fabien, M. Knepley, B. Rivière","doi":"10.1515/jnma-2019-0027","DOIUrl":"https://doi.org/10.1515/jnma-2019-0027","url":null,"abstract":"Abstract The focus of this paper is the analysis of families of hybridizable interior penalty discontinuous Galerkin methods for second order elliptic problems. We derive a priori error estimates in the energy norm that are optimal with respect to the mesh size. Suboptimal L2-norm error estimates are proven. These results are valid in two and three dimensions. Numerical results support our theoretical findings, and we illustrate the computational cost of the method.","PeriodicalId":50109,"journal":{"name":"Journal of Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2019-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79085944","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: 6
POD-ROM for the Darcy–Brinkman equations with double-diffusive convection 具有双扩散对流的Darcy-Brinkman方程的po - rom
IF 3 2区 数学
Journal of Numerical Mathematics Pub Date : 2019-09-01 DOI: 10.1515/jnma-2017-0122
Fatma G. Eroglu, Songul Kaya, L. Rebholz
{"title":"POD-ROM for the Darcy–Brinkman equations with double-diffusive convection","authors":"Fatma G. Eroglu, Songul Kaya, L. Rebholz","doi":"10.1515/jnma-2017-0122","DOIUrl":"https://doi.org/10.1515/jnma-2017-0122","url":null,"abstract":"Abstract This paper extends proper orthogonal decomposition reduced order modeling to flows governed by double diffusive convection, which models flow driven by two potentials with different rates of diffusion. We propose a reduced model based on proper orthogonal decomposition, present a stability and convergence analyses for it, and give results for numerical tests on a benchmark problem which show it is an effective approach to model reduction in this setting.","PeriodicalId":50109,"journal":{"name":"Journal of Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82368818","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: 12
Superconvergent discontinuous Galerkin methods for nonlinear parabolic initial and boundary value problems 非线性抛物型初值和边值问题的超收敛不连续Galerkin方法
IF 3 2区 数学
Journal of Numerical Mathematics Pub Date : 2019-09-01 DOI: 10.1515/jnma-2018-0035
Sangita Yadav, A. K. Pani
{"title":"Superconvergent discontinuous Galerkin methods for nonlinear parabolic initial and boundary value problems","authors":"Sangita Yadav, A. K. Pani","doi":"10.1515/jnma-2018-0035","DOIUrl":"https://doi.org/10.1515/jnma-2018-0035","url":null,"abstract":"Abstract In this article, we discuss error estimates for nonlinear parabolic problems using discontinuous Galerkin methods which include HDG method in the spatial direction while keeping time variable continuous. When piecewise polynomials of degree k ⩾ 1 are used to approximate both the potential as well as the flux, it is shown that the error estimate for the semi-discrete flux in L∞(0, T; L2)-norm is of order k + 1. With the help of a suitable post-processing of the semi-discrete potential, it is proved that the resulting post-processed potential converges with order of convergence O(log⁡(T/h2)hk+2) $begin{array}{} displaystyle Obig(!sqrt{{}log(T/h^2)},h^{k+2}big) end{array}$ in L∞(0, T; L2)-norm. These results extend the HDG analysis of Chabaud and Cockburn [Math. Comp. 81 (2012), 107–129] for the heat equation to non-linear parabolic problems.","PeriodicalId":50109,"journal":{"name":"Journal of Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75267711","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: 3
Inexact Newton method for the solution of eigenproblems arising in hydrodynamic temporal stability analysis 求解水动力时间稳定性分析中本征问题的非精确牛顿法
IF 3 2区 数学
Journal of Numerical Mathematics Pub Date : 2019-08-13 DOI: 10.1515/jnma-2019-0021
K. V. Demyanko, I. Kaporin, Y. Nechepurenko
{"title":"Inexact Newton method for the solution of eigenproblems arising in hydrodynamic temporal stability analysis","authors":"K. V. Demyanko, I. Kaporin, Y. Nechepurenko","doi":"10.1515/jnma-2019-0021","DOIUrl":"https://doi.org/10.1515/jnma-2019-0021","url":null,"abstract":"Abstract The inexact Newton method developed earlier for computing deflating subspaces associated with separated groups of finite eigenvalues of regular linear large sparse non-Hermitian matrix pencils is specialized to solve eigenproblems arising in the hydrodynamic temporal stability analysis. To this end, for linear systems to be solved at each step of the Newton method, a new efficient MLILU2 preconditioner based on the multilevel 2nd order incomplete LU-factorization is proposed. A special variant of Krylov subspace method IDR2 with right preconditioning is developed. In comparison with GMRES it requires much smaller workspace while may converge considerably faster than BiCGStab. The effectiveness of the proposed methods is illustrated with matrix pencils of order up to 3.1 ⋅ 106 arising in the temporal linear stability analysis of a typical hydrodinamic flow.","PeriodicalId":50109,"journal":{"name":"Journal of Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2019-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76307137","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: 2
Doubly-adaptive artificial compression methods for incompressible flow 不可压缩流的双自适应人工压缩方法
IF 3 2区 数学
Journal of Numerical Mathematics Pub Date : 2019-07-18 DOI: 10.1515/jnma-2019-0015
W. Layton, Michael McLaughlin
{"title":"Doubly-adaptive artificial compression methods for incompressible flow","authors":"W. Layton, Michael McLaughlin","doi":"10.1515/jnma-2019-0015","DOIUrl":"https://doi.org/10.1515/jnma-2019-0015","url":null,"abstract":"Abstract This report presents adaptive artificial compression methods in which the time-step and artificial compression parameter ε are independently adapted. The resulting algorithms are supported by analysis and numerical tests. The first and second-order methods are embedded. As a result, the computational, cognitive, and space complexities of the adaptive ε, k algorithms are negligibly greater than that of the simplest, first-order, constant ε, constant k artificial compression method.","PeriodicalId":50109,"journal":{"name":"Journal of Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2019-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74909974","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: 17
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：481959085
Book学术官方微信