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Full discretization error analysis of exponential integrators for semilinear wave equations 半线性波动方程指数积分器的全离散化误差分析
Math. Comput. Model. Pub Date : 2022-02-05 DOI: 10.1090/mcom/3736
Benjamin Dörich, Jan Leibold
{"title":"Full discretization error analysis of exponential integrators for semilinear wave equations","authors":"Benjamin Dörich, Jan Leibold","doi":"10.1090/mcom/3736","DOIUrl":"https://doi.org/10.1090/mcom/3736","url":null,"abstract":"In this article we prove full discretization error bounds for semilinear second-order evolution equations. We consider exponential integrators in time applied to an abstract nonconforming semi discretization in space. Since the fully discrete schemes involve the spatially discretized semigroup, a crucial point in the error analysis is to eliminate the continuous semigroup in the representation of the exact solution. Hence, we derive a modified variation-ofconstants formula driven by the spatially discretized semigroup which holds up to a discretization error. Our main results provide bounds for the full discretization errors for exponential Adams and explicit exponential Runge– Kutta methods. We show convergence with the stiff order of the corresponding exponential integrator in time, and errors stemming from the spatial discretization. As an application of the abstract theory, we consider an acoustic wave equation with kinetic boundary conditions, for which we also present some numerical experiments to illustrate our results.","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74842525","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
Fast and stable augmented Levin methods for highly oscillatory and singular integrals 高振荡和奇异积分的快速稳定增广Levin方法
Math. Comput. Model. Pub Date : 2022-01-14 DOI: 10.1090/mcom/3725
Yinkun Wang, S. Xiang
{"title":"Fast and stable augmented Levin methods for highly oscillatory and singular integrals","authors":"Yinkun Wang, S. Xiang","doi":"10.1090/mcom/3725","DOIUrl":"https://doi.org/10.1090/mcom/3725","url":null,"abstract":"","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86992497","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
A Trefftz method with reconstruction of the normal derivative applied to elliptic equations 带法向导数重建的Trefftz方法在椭圆方程中的应用
Math. Comput. Model. Pub Date : 2022-01-01 DOI: 10.1090/mcom/3756
B. Després, Maria El Ghaoui, Toni Sayah
{"title":"A Trefftz method with reconstruction of the normal derivative applied to elliptic equations","authors":"B. Després, Maria El Ghaoui, Toni Sayah","doi":"10.1090/mcom/3756","DOIUrl":"https://doi.org/10.1090/mcom/3756","url":null,"abstract":"There are many classical numerical methods for solving boundary value problems on general domains. The Trefftz method is an approximation method for solving linear boundary value problems arising in applied mathematics and engineering sciences. This method consists to approximate the exact solution through a linear combination of trial functions satisfying exactly the governing differential equation. One of the advantages of this method is that the number of trial functions per cell is O ( m ), asymp-totically much less than the quadratic estimate O ( m 2 ) for finite element and discontinuous Galerkin approximations. For a Laplace model equation, we present a high order Trefftz method with quadrature formula for calculation of normal derivative at interfaces. We introduce a discrete variational formulation and study the existence and uniqueness of the discrete solution. A priori error estimate is then established and finally, several numerical experiments are shown.","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":"85079395","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
Inf-sup stability implies quasi-orthogonality 上支撑稳定性意味着准正交性
Math. Comput. Model. Pub Date : 2022-01-01 DOI: 10.1090/mcom/3748
M. Feischl
{"title":"Inf-sup stability implies quasi-orthogonality","authors":"M. Feischl","doi":"10.1090/mcom/3748","DOIUrl":"https://doi.org/10.1090/mcom/3748","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":"89970651","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
An algorithm to recognize regular singular Mahler systems 正则奇异马勒系统的识别算法
Math. Comput. Model. Pub Date : 2022-01-01 DOI: 10.1090/mcom/3758
Colin Faverjon, Marina Poulet
{"title":"An algorithm to recognize regular singular Mahler systems","authors":"Colin Faverjon, Marina Poulet","doi":"10.1090/mcom/3758","DOIUrl":"https://doi.org/10.1090/mcom/3758","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":"88574625","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
Density function of numerical solution of splitting AVF scheme for stochastic Langevin equation 随机朗之万方程分裂AVF格式数值解的密度函数
Math. Comput. Model. Pub Date : 2022-01-01 DOI: 10.1090/mcom/3752
J. Cui, Jialin Hong, Derui Sheng
{"title":"Density function of numerical solution of splitting AVF scheme for stochastic Langevin equation","authors":"J. Cui, Jialin Hong, Derui Sheng","doi":"10.1090/mcom/3752","DOIUrl":"https://doi.org/10.1090/mcom/3752","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":"76044931","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: 4
Error estimates for discrete generalized FEMs with locally optimal spectral approximations 具有局部最优谱近似的离散广义fem误差估计
Math. Comput. Model. Pub Date : 2022-01-01 DOI: 10.1090/mcom/3755
Chupeng Ma, Robert Scheichl
{"title":"Error estimates for discrete generalized FEMs with locally optimal spectral approximations","authors":"Chupeng Ma, Robert Scheichl","doi":"10.1090/mcom/3755","DOIUrl":"https://doi.org/10.1090/mcom/3755","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":"90445565","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
An algorithm for Hodge ideals 霍奇理想的算法
Math. Comput. Model. Pub Date : 2022-01-01 DOI: 10.1090/mcom/3764
Guillem Blanco
{"title":"An algorithm for Hodge ideals","authors":"Guillem Blanco","doi":"10.1090/mcom/3764","DOIUrl":"https://doi.org/10.1090/mcom/3764","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":"74720472","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
Anti-Gaussian quadrature formulae of Chebyshev type 切比雪夫型反高斯正交公式
Math. Comput. Model. Pub Date : 2022-01-01 DOI: 10.1090/mcom/3762
Sotirios E. Notaris
{"title":"Anti-Gaussian quadrature formulae of Chebyshev type","authors":"Sotirios E. Notaris","doi":"10.1090/mcom/3762","DOIUrl":"https://doi.org/10.1090/mcom/3762","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":"87275007","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
Delay-dependent elliptic reconstruction and optimal L∞ (L2) a posteriori error estimates for fully discrete delay parabolic problems 全离散时滞抛物型问题的时滞相关椭圆重构和最优L∞(L2)后验误差估计
Math. Comput. Model. Pub Date : 2022-01-01 DOI: 10.1090/mcom/3761
Wansheng Wang, Lijun Yi
{"title":"Delay-dependent elliptic reconstruction and optimal L∞ (L2) a posteriori error estimates for fully discrete delay parabolic problems","authors":"Wansheng Wang, Lijun Yi","doi":"10.1090/mcom/3761","DOIUrl":"https://doi.org/10.1090/mcom/3761","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":"85377657","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: 2
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