arXiv: Numerical Analysis最新文献_第2页

A Numerical Approach for Solving of Fractional Emden-Fowler Type Equations 求解分数阶Emden-Fowler型方程的数值方法

arXiv: Numerical Analysis Pub Date : 2019-01-08 DOI: 10.1063/1.5043786

J. Rebenda, Zdenvek vSmarda

引用次数: 4

Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction–diffusion problems 奇摄动反应扩散问题的简单鲁棒平衡通量后验估计

arXiv: Numerical Analysis Pub Date : 2018-12-17 DOI: 10.1051/m2an/2020034

Iain Smears, Martin Vohral'ik

{"title":"Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction–diffusion problems","authors":"Iain Smears, Martin Vohral'ik","doi":"10.1051/m2an/2020034","DOIUrl":"https://doi.org/10.1051/m2an/2020034","url":null,"abstract":"We consider energy norm a posteriori error analysis of conforming finite element approximations of singularly perturbed reaction-diffusion problems on simplicial meshes in arbitrary space dimension. Using an equilibrated flux reconstruction, the proposed estimator gives a guaranteed global upper bound on the error without unknown constants, and local efficiency robust with respect to the mesh size and singular perturbation parameters. Whereas previous works on equilibrated flux estimators only considered lowest-order finite element approximations and achieved robustness through the use of boundary-layer adapted submeshes or via combination with residual-based estimators, the present methodology applies in a simple way to arbitrary-order approximations and does not request any submesh or estimators combination. The equilibrated flux is obtained via local reaction-diffusion problems with suitable weights (cut-off factors), and the guaranteed upper bound features the same weights. We prove that the inclusion of these weights is not only sufficient but also necessary for robustness of any flux equilibration estimate that does not employ submeshes or estimators combination, which shows that some of the flux equilibrations proposed in the past cannot be robust. To achieve the fully computable upper bound, we derive explicit bounds for some inverse inequality constants on a simplex, which may be of independent interest.","PeriodicalId":283112,"journal":{"name":"arXiv: Numerical Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130780117","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: 11

Recursive Process for Constructing the Refinement Rules of New Combined Subdivision Schemes and Its Extended Form 构造新组合细分方案细化规则的递归过程及其扩展形式

arXiv: Numerical Analysis Pub Date : 2018-12-04 DOI: 10.1155/2021/6639706

Rabia Hameed, G. Mustafa, J. Deng, Shafqat Ali

引用次数: 2

Reduced Order Isogeometric Analysis Approach for PDEs in Parametrized Domains 参数化域偏微分方程的降阶等几何分析方法

arXiv: Numerical Analysis Pub Date : 2018-11-21 DOI: 10.1007/978-3-030-48721-8_7

Fabrizio Garotta, N. Demo, M. Tezzele, M. Carraturo, A. Reali, G. Rozza

引用次数: 19

A Parallel Solver for a Preconditioned Space-Time Boundary Element Method for the Heat Equation 热方程的预条件时空边界元法并行求解器

arXiv: Numerical Analysis Pub Date : 2018-11-13 DOI: 10.1007/978-3-030-56750-7_11

S. Dohr, M. Merta, G. Of, O. Steinbach, Jan Zapletal

引用次数: 7

On Wielandt-Mirsky's conjecture for matrix polynomials 关于矩阵多项式的Wielandt-Mirsky猜想

arXiv: Numerical Analysis Pub Date : 2018-11-08 DOI: 10.4134/BKMS.B181065

C. Lê

引用次数: 3

An integrated data-driven computational pipeline with model order reduction for industrial and applied mathematics 一种集成数据驱动的模型降阶计算管道，用于工业数学和应用数学

arXiv: Numerical Analysis Pub Date : 2018-10-29 DOI: 10.1007/978-3-030-96173-2_7

M. Tezzele, N. Demo, A. Mola, G. Rozza

引用次数: 27

A New Parareal Algorithm for Time-Periodic Problems with Discontinuous Inputs 输入不连续时周期问题的一种新的拟面算法

arXiv: Numerical Analysis Pub Date : 2018-10-29 DOI: 10.1007/978-3-030-56750-7_27

M. Gander, Iryna Kulchytska-Ruchka, S. Schops

引用次数: 5

A Mass-Lumped Mixed Finite Element Method for Maxwell’s Equations 麦克斯韦方程组的质量集总混合有限元法

arXiv: Numerical Analysis Pub Date : 2018-10-15 DOI: 10.1007/978-3-030-44101-2_2

H. Egger, B. Radu

引用次数: 6

Downwinding for Preserving Strong Stability in Explicit Integrating Factor Runge--Kutta Methods 显式积分因子Runge—Kutta方法中保持强稳定性的下卷

arXiv: Numerical Analysis Pub Date : 2018-10-10 DOI: 10.4310/PAMQ.2018.V14.N1.A1

Leah Isherwood, Zachary J. Grant, S. Gottlieb

{"title":"Downwinding for Preserving Strong Stability in Explicit Integrating Factor Runge--Kutta Methods","authors":"Leah Isherwood, Zachary J. Grant, S. Gottlieb","doi":"10.4310/PAMQ.2018.V14.N1.A1","DOIUrl":"https://doi.org/10.4310/PAMQ.2018.V14.N1.A1","url":null,"abstract":"Strong stability preserving (SSP) Runge-Kutta methods are desirable when evolving in time problems that have discontinuities or sharp gradients and require nonlinear non-inner-product stability properties to be satisfied. Unlike the case for L2 linear stability, implicit methods do not significantly alleviate the time-step restriction when the SSP property is needed. For this reason, when handling problems with a linear component that is stiff and a nonlinear component that is not, SSP integrating factor Runge--Kutta methods may offer an attractive alternative to traditional time-stepping methods. The strong stability properties of integrating factor Runge--Kutta methods where the transformed problem is evolved with an explicit SSP Runge--Kutta method with non-decreasing abscissas was recently established. In this work, we consider the use of downwinded spatial operators to preserve the strong stability properties of integrating factor Runge--Kutta methods where the Runge--Kutta method has some decreasing abscissas. We present the SSP theory for this approach and present numerical evidence to show that such an approach is feasible and performs as expected. However, we also show that in some cases the integrating factor approach with explicit SSP Runge--Kutta methods with non-decreasing abscissas performs nearly as well, if not better, than with explicit SSP Runge--Kutta methods with downwinding. In conclusion, while the downwinding approach can be rigorously shown to guarantee the SSP property for a larger time-step, in practice using the integrating factor approach by including downwinding as needed with optimal explicit SSP Runge--Kutta methods does not necessarily provide significant benefit over using explicit SSP Runge--Kutta methods with non-decreasing abscissas.","PeriodicalId":283112,"journal":{"name":"arXiv: Numerical Analysis","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132477575","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