Advances in Computational Mathematics最新文献

Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies 亥姆霍兹有限元求解在低频局部准最优

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-11-18 DOI: 10.1007/s10444-024-10193-w

M. Averseng, J. Galkowski, E. A. Spence

{"title":"Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies","authors":"M. Averseng, J. Galkowski, E. A. Spence","doi":"10.1007/s10444-024-10193-w","DOIUrl":"10.1007/s10444-024-10193-w","url":null,"abstract":"<div>For h-FEM discretisations of the Helmholtz equation with wavenumber k, we obtain k-explicit analogues of the classic local FEM error bounds of Nitsche and Schatz (Math. Comput. 28(128), 937–958 1974), Wahlbin (1991, §9), Demlow et al.(Math. Comput. 80(273), 1–9 2011), showing that these bounds hold with constants independent of k, provided one works in Sobolev norms weighted with k in the natural way. We prove two main results: (i) a bound on the local (H^1) error by the best approximation error plus the (L^2) error, both on a slightly larger set, and (ii) the bound in (i) but now with the (L^2) error replaced by the error in a negative Sobolev norm. The result (i) is valid for shape-regular triangulations, and is the k-explicit analogue of the main result of Demlow et al. (Math. Comput. 80(273), 1–9 2011). The result (ii) is valid when the mesh is locally quasi-uniform on the scale of the wavelength (i.e., on the scale of (k^{-1})) and is the k-explicit analogue of the results of Nitsche and Schatz (Math. Comput. 28(128), 937–958 1974), Wahlbin (1991, §9). Since our Sobolev spaces are weighted with k in the natural way, the result (ii) indicates that the Helmholtz FEM solution is locally quasi-optimal modulo low frequencies (i.e., frequencies (lesssim k)). Numerical experiments confirm this property, and also highlight interesting propagation phenomena in the Helmholtz FEM error.</div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 6","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10193-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142664470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Higher-order iterative decoupling for poroelasticity 孔弹性的高阶迭代解耦

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-11-15 DOI: 10.1007/s10444-024-10200-0

Robert Altmann, Abdullah Mujahid, Benjamin Unger

引用次数: 0

Adaptive quarklet tree approximation 自适应夸克树近似法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-10-31 DOI: 10.1007/s10444-024-10205-9

Stephan Dahlke, Marc Hovemann, Thorsten Raasch, Dorian Vogel

引用次数: 0

Efficient computation of the sinc matrix function for the integration of second-order differential equations 高效计算用于二阶微分方程积分的 sinc 矩阵函数

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-10-28 DOI: 10.1007/s10444-024-10202-y

Lidia Aceto, Fabio Durastante

引用次数: 0

Sobolev regularity of bivariate isogeometric finite element spaces in case of a geometry map with degenerate corner 双变量等几何有限元空间在有退化角几何图形情况下的索波列夫正则性

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-10-24 DOI: 10.1007/s10444-024-10203-x

Ulrich Reif

引用次数: 0

An optimal ansatz space for moving least squares approximation on spheres 球面移动最小二乘法近似的最佳解析空间

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-10-22 DOI: 10.1007/s10444-024-10201-z

Ralf Hielscher, Tim Pöschl

引用次数: 0

A unified local projection-based stabilized virtual element method for the coupled Stokes-Darcy problem 斯托克斯-达西耦合问题的基于局部投影的统一稳定虚拟元素法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-10-21 DOI: 10.1007/s10444-024-10199-4

Sudheer Mishra, E. Natarajan

引用次数: 0

A pressure-residual augmented GLS stabilized method for a type of Stokes equations with nonstandard boundary conditions 具有非标准边界条件的斯托克斯方程类型的压力-滞后增强 GLS 稳定方法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-10-14 DOI: 10.1007/s10444-024-10204-w

Huoyuan Duan, Roger C. E. Tan, Duowei Zhu

{"title":"A pressure-residual augmented GLS stabilized method for a type of Stokes equations with nonstandard boundary conditions","authors":"Huoyuan Duan, Roger C. E. Tan, Duowei Zhu","doi":"10.1007/s10444-024-10204-w","DOIUrl":"10.1007/s10444-024-10204-w","url":null,"abstract":"<div>With local pressure-residual stabilizations as an augmentation to the classical Galerkin/least-squares (GLS) stabilized method, a new locally evaluated residual-based stabilized finite element method is proposed for a type of Stokes equations from the incompressible flows. We focus on the study of a type of nonstandard boundary conditions involving the mixed tangential velocity and pressure Dirichlet boundary conditions. Unexpectedly, in sharp contrast to the standard no-slip velocity Dirichlet boundary condition, neither the discrete LBB inf-sup stable elements nor the stabilized methods such as the classical GLS method could certainly ensure a convergent finite element solution, because the velocity solution could be very weak with its gradient not being square integrable. The main purpose of this paper is to study the error estimates of the new stabilized method for approximating the very weak velocity solution; with the local pressure-residual stabilizations, we can manage to prove the error estimates with a reasonable convergence order. Numerical results are provided to illustrate the performance and the theoretical results of the proposed method.</div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

A stochastic perturbation analysis of the QR decomposition and its applications QR 分解的随机扰动分析及其应用

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-10-02 DOI: 10.1007/s10444-024-10198-5

Tianru Wang, Yimin Wei

引用次数: 0

An electrical engineering perspective on naturality in computational physics 从电气工程角度看计算物理学的自然性

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-10-01 DOI: 10.1007/s10444-024-10197-6

P. Robert Kotiuga, Valtteri Lahtinen

引用次数: 0