arXiv: Numerical Analysis最新文献_第10页

A Priori and A Posteriori Error Control of Discontinuous Galerkin Finite Element Methods for the Von K'arm'an Equations 冯k臂方程不连续Galerkin有限元法的先验和后验误差控制

arXiv: Numerical Analysis Pub Date : 2017-08-25 DOI: 10.1093/IMANUM/DRY003

C. Carstensen, Gouranga Mallik, N. Nataraj

{"title":"A Priori and A Posteriori Error Control of Discontinuous Galerkin Finite Element Methods for the Von K'arm'an Equations","authors":"C. Carstensen, Gouranga Mallik, N. Nataraj","doi":"10.1093/IMANUM/DRY003","DOIUrl":"https://doi.org/10.1093/IMANUM/DRY003","url":null,"abstract":"This paper analyses discontinuous Galerkin finite element methods (DGFEM) to approximate a regular solution to the von Karman equations defined on a polygonal domain. A discrete inf-sup condition sufficient for the stability of the discontinuous Galerkin discretization of a well-posed linear problem is established and this allows the proof of local existence and uniqueness of a discrete solution to the non-linear problem with a Banach fixed point theorem. The Newton scheme is locally second-order convergent and appears to be a robust solution strategy up to machine precision. A comprehensive a priori and a posteriori energy-norm error analysis relies on one sufficiently large stabilization parameter and sufficiently fine triangulations. In case the other stabilization parameter degenerates towards infinity, the DGFEM reduces to a novel $C^0$ interior penalty method (IPDG). Moreover, a reliable and efficient a posteriori error analysis immediately follows for the DGFEM of this paper, while the different norms in the known $C^0$-IPDG lead to complications with some non-residual type remaining terms. Numerical experiments confirm the best-approximation results and the equivalence of the error and the error estimators. A related adaptive mesh-refining algorithm leads to optimal empirical convergence rates for a non convex domain.","PeriodicalId":283112,"journal":{"name":"arXiv: Numerical Analysis","volume":"198 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114618041","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: 16

Construction of a $C^2$ class finite element based on the Clough-Tocher subdivision 基于Clough-Tocher细分的$C^2$类有限元构造

arXiv: Numerical Analysis Pub Date : 2017-08-23 DOI: 10.17654/nm016340157

Haudi'e Jean St'ephane Inkp'e, K. B. J. Claude, A. L. M'ehaut'e

引用次数: 0

Balanced data assimilation for highly oscillatory mechanical systems 高振荡机械系统的平衡数据同化

arXiv: Numerical Analysis Pub Date : 2017-08-11 DOI: 10.2140/camcos.2021.16.119

G. Hastermann, Maria Reinhardt, R. Klein, S. Reich

{"title":"Balanced data assimilation for highly oscillatory mechanical systems","authors":"G. Hastermann, Maria Reinhardt, R. Klein, S. Reich","doi":"10.2140/camcos.2021.16.119","DOIUrl":"https://doi.org/10.2140/camcos.2021.16.119","url":null,"abstract":"Data assimilation algorithms are used to estimate the states of a dynamical system using partial and noisy observations. The ensemble Kalman filter has become a popular data assimilation scheme due to its simplicity and robustness for a wide range of application areas. Nevertheless, the ensemble Kalman filter also has limitations due to its inherent Gaussian and linearity assumptions. These limitations can manifest themselves in dynamically inconsistent state estimates. We investigate this issue in this paper for highly oscillatory Hamiltonian systems with a dynamical behavior which satisfies certain balance relations. We first demonstrate that the standard ensemble Kalman filter can lead to estimates which do not satisfy those balance relations, ultimately leading to filter divergence. We also propose two remedies for this phenomenon in terms of blended time-stepping schemes and ensemble-based penalty methods. The effect of these modifications to the standard ensemble Kalman filter are discussed and demonstrated numerically for two model scenarios. First, we consider balanced motion for highly oscillatory Hamiltonian systems and, second, we investigate thermally embedded highly oscillatory Hamiltonian systems. The first scenario is relevant for applications from meteorology while the second scenario is relevant for applications of data assimilation to molecular dynamics.","PeriodicalId":283112,"journal":{"name":"arXiv: Numerical Analysis","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126660810","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

Heuristic Parameter Choice in Tikhonov Method from Minimizers of the Quasi-Optimality Function 拟最优函数极小值下Tikhonov方法的启发式参数选择

arXiv: Numerical Analysis Pub Date : 2017-08-07 DOI: 10.1007/978-3-319-70824-9_12

T. Raus, U. Hamarik

引用次数: 7

Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains 多边形域上积分分数阶拉普拉斯算子的有效有限元方法

arXiv: Numerical Analysis Pub Date : 2017-08-06 DOI: 10.1007/978-3-319-72456-0_2

M. Ainsworth, Christian A. Glusa

引用次数: 59

Probabilistic Lower Bounds for the Discrepancy of Latin Hypercube Samples 拉丁超立方体样本差异的概率下界

arXiv: Numerical Analysis Pub Date : 2017-07-26 DOI: 10.1007/978-3-319-72456-0_16

Benjamin Doerr, Carola Doerr, M. Gnewuch