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Error estimates for a class of continuous Bonse-type inequalities 一类连续bonse型不等式的误差估计
Math. Comput. Model. Pub Date : 2022-01-01 DOI: 10.1090/mcom/3741
D. Marques, P. Trojovský
{"title":"Error estimates for a class of continuous Bonse-type inequalities","authors":"D. Marques, P. Trojovský","doi":"10.1090/mcom/3741","DOIUrl":"https://doi.org/10.1090/mcom/3741","url":null,"abstract":"","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76407424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Algorithms for fundamental invariants and equivariants of finite groups 有限群的基本不变量和等变算法
Math. Comput. Model. Pub Date : 2022-01-01 DOI: 10.1090/mcom/3749
E. Hubert, Erick D. Rodríguez Bazan
{"title":"Algorithms for fundamental invariants and equivariants of finite groups","authors":"E. Hubert, Erick D. Rodríguez Bazan","doi":"10.1090/mcom/3749","DOIUrl":"https://doi.org/10.1090/mcom/3749","url":null,"abstract":"","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73634498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
A symmetric low-regularity integrator for nonlinear Klein-Gordon equation 非线性Klein-Gordon方程的对称低正则积分器
Math. Comput. Model. Pub Date : 2022-01-01 DOI: 10.1090/mcom/3751
Yan Wang, Xiaofei Zhao
{"title":"A symmetric low-regularity integrator for nonlinear Klein-Gordon equation","authors":"Yan Wang, Xiaofei Zhao","doi":"10.1090/mcom/3751","DOIUrl":"https://doi.org/10.1090/mcom/3751","url":null,"abstract":"","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82675035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Finite element/holomorphic operator function method for the transmission eigenvalue problem 传输特征值问题的有限元/全纯算子函数方法
Math. Comput. Model. Pub Date : 2022-01-01 DOI: 10.1090/mcom/3767
Bo Gong, Jiguang Sun, T. Turner, Chunxiong Zheng
{"title":"Finite element/holomorphic operator function method for the transmission eigenvalue problem","authors":"Bo Gong, Jiguang Sun, T. Turner, Chunxiong Zheng","doi":"10.1090/mcom/3767","DOIUrl":"https://doi.org/10.1090/mcom/3767","url":null,"abstract":"","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73094539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Maximum-norm stability of the finite element method for the Neumann problem in nonconvex polygons with locally refined mesh 局部精细网格非凸多边形Neumann问题的有限元法的最大范数稳定性
Math. Comput. Model. Pub Date : 2021-12-31 DOI: 10.1090/mcom/3724
Buyang Li
{"title":"Maximum-norm stability of the finite element method for the Neumann problem in nonconvex polygons with locally refined mesh","authors":"Buyang Li","doi":"10.1090/mcom/3724","DOIUrl":"https://doi.org/10.1090/mcom/3724","url":null,"abstract":"The Galerkin finite element solution uh of the Possion equation −∆u = f under the Neumann boundary condition in a possibly nonconvex polygon Ω, with a graded mesh locally refined at the corners of the domain, is shown to satisfy the following maximum-norm stability: ‖uh‖L∞(Ω) ≤ C`h‖u‖L∞(Ω), where `h = ln(2+1/h) for piecewise linear elements and `h = 1 for higher-order elements. As a result of the maximum-norm stability, the following best approximation result holds: ‖u− uh‖L∞(Ω) ≤ C`h‖u− Ihu‖L∞(Ω), where Ih denotes the Lagrange interpolation operator onto the finite element space. For a locally quasi-uniform triangulation sufficiently refined at the corners, the above best approximation property implies the following optimal-order error bound in the maximum norm: ‖u− uh‖L∞(Ω) ≤ { C`hh k+2− 2 p ‖f‖Wk,p(Ω) if r ≥ k + 1, C`hh ‖f‖Hk(Ω) if r = k, where r ≥ 1 is the degree of finite elements, k is any nonnegative integer no larger than r, and p ∈ [2,∞) can be arbitrarily large.","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82742442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
A posteriori error analysis for approximations of time-fractional subdiffusion problems 时间分数次扩散问题近似的后验误差分析
Math. Comput. Model. Pub Date : 2021-12-30 DOI: 10.1090/mcom/3723
L. Banjai, C. Makridakis
{"title":"A posteriori error analysis for approximations of time-fractional subdiffusion problems","authors":"L. Banjai, C. Makridakis","doi":"10.1090/mcom/3723","DOIUrl":"https://doi.org/10.1090/mcom/3723","url":null,"abstract":"In this paper we consider a sub-diffusion problem where the fractional time derivative is approximated either by the L1 scheme or by Convolution Quadrature. We propose new interpretations of the numerical schemes which lead to a posteriori error estimates. Our approach is based on appropriate pointwise representations of the numerical schemes as perturbed evolution equations and on stability estimates for the evolution equation. A posteriori error estimates in $L^2(H)$ and $L^infty (H)$ norms of optimal order are derived. Extensive numerical experiments indicate the reliability and the optimality of the estimators for the schemes considered, as well as their efficiency as error indicators driving adaptive mesh selection locating singularities of the problem.","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81776078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Strictly convex entropy and entropy stable schemes for reactive Euler equations 反应性欧拉方程的严格凸熵和熵稳定格式
Math. Comput. Model. Pub Date : 2021-12-16 DOI: 10.1090/mcom/3721
Weifeng Zhao
{"title":"Strictly convex entropy and entropy stable schemes for reactive Euler equations","authors":"Weifeng Zhao","doi":"10.1090/mcom/3721","DOIUrl":"https://doi.org/10.1090/mcom/3721","url":null,"abstract":"This paper presents entropy analysis and entropy stable (ES) finite difference schemes for the reactive Euler equations with chemical reactions. For such equations we point out that the thermodynamic entropy is no longer strictly convex. To address this issue, we propose a strictly convex entropy function by adding an extra term to the thermodynamic entropy. Thanks to the strict convexity of the proposed entropy, the Roe-type dissipation operator in terms of the entropy variables can be formulated. Furthermore, we construct two sets of second-order entropy preserving (EP) numerical fluxes for the reactive Euler equations. Based on the EP fluxes and the Roe-type dissipation operators, high-order EP/ES fluxes are derived. Numerical experiments validate the designed accuracy and good performance of our schemes for smooth and discontinuous initial value problems. The entropy decrease of ES schemes is verified as well.","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91232547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Four consecutive primitive elementsin a finite field 有限域中四个连续的基本元素
Math. Comput. Model. Pub Date : 2021-11-24 DOI: 10.1090/mcom/3716
Tamiru Jarso, T. Trudgian
{"title":"Four consecutive primitive elementsin a finite field","authors":"Tamiru Jarso, T. Trudgian","doi":"10.1090/mcom/3716","DOIUrl":"https://doi.org/10.1090/mcom/3716","url":null,"abstract":"","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78905703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Why large time-stepping methods for the Cahn-Hilliard equation is stable 为什么大时间步进法求解Cahn-Hilliard方程是稳定的
Math. Comput. Model. Pub Date : 2021-11-11 DOI: 10.1090/mcom/3768
Dong Li
{"title":"Why large time-stepping methods for the Cahn-Hilliard equation is stable","authors":"Dong Li","doi":"10.1090/mcom/3768","DOIUrl":"https://doi.org/10.1090/mcom/3768","url":null,"abstract":"We consider the Cahn-Hilliard equation with standard double-well potential. We employ a prototypical class of first order in time semi-implicit methods with implicit treatment of the linear dissipation term and explicit extrapolation of the nonlinear term. When the dissipation coefficient is held small, a conventional wisdom is to add a judiciously chosen stabilization term in order to afford relatively large time stepping and speed up the simulation. In practical numerical implementations it has been long observed that the resulting system exhibits remarkable stability properties in the regime where the stabilization parameter is O(1), the dissipation coefficient is vanishingly small and the size of the time step is moderately large. In this work we develop a new stability theory to address this perplexing phenomenon.","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82291311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Stochastic gradient descent for linear inverse problems in Hilbert spaces Hilbert空间中线性逆问题的随机梯度下降
Math. Comput. Model. Pub Date : 2021-11-06 DOI: 10.1090/mcom/3714
Shuai Lu, P. Mathé
{"title":"Stochastic gradient descent for linear inverse problems in Hilbert spaces","authors":"Shuai Lu, P. Mathé","doi":"10.1090/mcom/3714","DOIUrl":"https://doi.org/10.1090/mcom/3714","url":null,"abstract":"","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81897724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
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