SIAM Journal on Numerical Analysis最新文献_第6页

Numerical Reconstruction of Diffusion and Potential Coefficients from Two Observations: Decoupled Recovery and Error Estimates 根据两次观测结果数值重构扩散系数和电位系数：解耦恢复和误差估计

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-10-03 DOI: 10.1137/23m1590743

Siyu Cen, Zhi Zhou

{"title":"Numerical Reconstruction of Diffusion and Potential Coefficients from Two Observations: Decoupled Recovery and Error Estimates","authors":"Siyu Cen, Zhi Zhou","doi":"10.1137/23m1590743","DOIUrl":"https://doi.org/10.1137/23m1590743","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2276-2307, October 2024. <br/> Abstract. The focus of this paper is on the concurrent reconstruction of both the diffusion and potential coefficients present in an elliptic/parabolic equation, utilizing two internal measurements of the solutions. A decoupled algorithm is constructed to sequentially recover these two parameters. In the first step, we implement a straightforward reformulation that results in a standard problem of identifying the diffusion coefficient. This coefficient is then numerically recovered, with no requirement for knowledge of the potential, by utilizing an output least-squares method coupled with finite element discretization. In the second step, the previously recovered diffusion coefficient is employed to reconstruct the potential coefficient, applying a method similar to the first step. Our approach is stimulated by a constructive conditional stability, and we provide rigorous a priori error estimates in [math] for the recovered diffusion and potential coefficients. To derive these estimates, we develop a weighted energy argument and suitable positivity conditions. These estimates offer a beneficial guide for choosing regularization parameters and discretization mesh sizes, in accordance with the noise level. Some numerical experiments are presented to demonstrate the accuracy of the numerical scheme and support our theoretical results.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"26 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142369295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

On the Optimality of Target-Data-Dependent Kernel Greedy Interpolation in Sobolev Reproducing Kernel Hilbert Spaces 论索博廖夫重现核希尔伯特空间中目标数据依赖核贪婪插值的最优性

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-09-23 DOI: 10.1137/23m1587956

Gabriele Santin, Tizian Wenzel, Bernard Haasdonk

{"title":"On the Optimality of Target-Data-Dependent Kernel Greedy Interpolation in Sobolev Reproducing Kernel Hilbert Spaces","authors":"Gabriele Santin, Tizian Wenzel, Bernard Haasdonk","doi":"10.1137/23m1587956","DOIUrl":"https://doi.org/10.1137/23m1587956","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2249-2275, October 2024. <br/> Abstract. Kernel interpolation is a versatile tool for the approximation of functions from data, and it can be proven to have some optimality properties when used with kernels related to certain Sobolev spaces. In the context of interpolation, the selection of optimal function sampling locations is a central problem, both from a practical perspective and as an interesting theoretical question. Greedy interpolation algorithms provide a viable solution for this task, being efficient to run and provably accurate in their approximation. In this paper we close a gap that is present in the convergence theory for these algorithms by employing a recent result on general greedy algorithms. This modification leads to new convergence rates which match the optimal ones when restricted to the [math]-greedy target-data-independent selection rule and can additionally be proven to be optimal when they fully exploit adaptivity ([math]-greedy). Other than closing this gap, the new results have some significance in the broader setting of the optimality of general approximation algorithms in reproducing kernel Hilbert spaces, as they allow us to compare adaptive interpolation with nonadaptive best nonlinear approximation.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"31 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142313711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Analysis of Local Discontinuous Galerkin Methods with Implicit-Explicit Time Marching for Linearized KdV Equations 针对线性化 KdV 方程的隐式-显式时间行进局部非连续伽勒金方法分析

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-09-19 DOI: 10.1137/24m1635818

Haijin Wang, Qi Tao, Chi-Wang Shu, Qiang Zhang

{"title":"Analysis of Local Discontinuous Galerkin Methods with Implicit-Explicit Time Marching for Linearized KdV Equations","authors":"Haijin Wang, Qi Tao, Chi-Wang Shu, Qiang Zhang","doi":"10.1137/24m1635818","DOIUrl":"https://doi.org/10.1137/24m1635818","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2222-2248, October 2024. <br/> Abstract. In this paper, we present the stability and error analysis of two fully discrete IMEX-LDG schemes, combining local discontinuous Galerkin spatial discretization with implicit-explicit Runge–Kutta temporal discretization, for the linearized one-dimensional KdV equations. The energy stability analysis begins with a series of temporal differences about stage solutions. Then by exploring the stability mechanism from the temporal differences, and by constructing the seminegative definite symmetric form related to the discretization of the dispersion term, and by adopting the important relationships between the auxiliary variables with the prime variable to control the antidissipation terms, we derive the unconditional stability for a discrete energy involving the prime variable and all the auxiliary variables, in the sense that the time step is bounded by a constant that is independent of the spatial mesh size. We also propose a new projection technique and adopt the technique of summation by parts in the time direction to achieve the optimal order of accuracy. The new projection technique can serve as an analytical tool to be applied to general odd order wave equations. Finally, numerical experiments are shown to test the stability and accuracy of the considered schemes.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"119 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142276030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Some Grönwall Inequalities for a Class of Discretizations of Time Fractional Equations on Nonuniform Meshes 非均匀网格上一类时间分式方程离散化的一些格伦沃尔不等式

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-09-18 DOI: 10.1137/24m1631614

Yuanyuan Feng, Lei Li, Jian-Guo Liu, Tao Tang

引用次数: 0

A Convergent Evolving Finite Element Method with Artificial Tangential Motion for Surface Evolution under a Prescribed Velocity Field 利用人工切向运动的收敛性演化有限元方法，解决规定速度场下的表面演化问题

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-09-17 DOI: 10.1137/23m156968x

Genming Bai, Jiashun Hu, Buyang Li

引用次数: 0

Numerical Schemes for Coupled Systems of Nonconservative Hyperbolic Equations 非守恒双曲方程耦合系统的数值方案

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-09-11 DOI: 10.1137/23m1615176

Niklas Kolbe, Michael Herty, Siegfried Müller

{"title":"Numerical Schemes for Coupled Systems of Nonconservative Hyperbolic Equations","authors":"Niklas Kolbe, Michael Herty, Siegfried Müller","doi":"10.1137/23m1615176","DOIUrl":"https://doi.org/10.1137/23m1615176","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2143-2171, October 2024. <br/> Abstract. The coupling of nonconservative hyperbolic systems at a static interface has been a delicate issue as common approaches rely on the Lax-curves of the systems, which are not always available. To address this a new linear relaxation system is introduced, in which a nonlocal source term accounts for the nonconservative product of the original system. Using an asymptotic analysis the relaxation limit and its stability are investigated in the uncoupled setting. It is shown that the path-conservative Lax–Friedrichs scheme arises from a discrete limit of an implicit-explicit scheme for the relaxation system. Employing the relaxation approach, a novel technique to couple two nonconservative systems under a large class of coupling conditions is established. A particular coupling strategy motivated from conservative Kirchhoff conditions is introduced and a corresponding Riemann solver provided. A fully discrete scheme for coupled nonconservative products is derived and studied in terms of path conservation. Numerical experiments applying the approach to a coupled model of vascular blood flow are presented.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"130 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142166257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Two-Scale Finite Element Approximation of a Homogenized Plate Model 均质板模型的双尺度有限元逼近

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-09-11 DOI: 10.1137/23m1596272

Martin Rumpf, Stefan Simon, Christoph Smoch

引用次数: 0

Error Analysis Based on Inverse Modified Differential Equations for Discovery of Dynamics Using Linear Multistep Methods and Deep Learning 基于逆修正微分方程的误差分析，利用线性多步骤方法和深度学习发现动力学规律

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-09-04 DOI: 10.1137/22m152373x

Aiqing Zhu, Sidi Wu, Yifa Tang

引用次数: 0

Low Regularity Full Error Estimates for the Cubic Nonlinear Schrödinger Equation 立方非线性薛定谔方程的低正则全误差估计

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-09-03 DOI: 10.1137/23m1619617

Lun Ji, Alexander Ostermann, Frédéric Rousset, Katharina Schratz

引用次数: 0

New Time Domain Decomposition Methods for Parabolic Optimal Control Problems I: Dirichlet–Neumann and Neumann–Dirichlet Algorithms 抛物线最优控制问题的新时域分解方法 I. Dirichlet-Neumann 和 Neumann-Dirichlet 算法Dirichlet-Neumann 和 Neumann-Dirichlet 算法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-08-23 DOI: 10.1137/23m1584502

Martin J. Gander, Liu-Di Lu

引用次数: 0