SIAM Journal on Numerical Analysis最新文献

Optimality of Quasi-Monte Carlo Methods and Suboptimality of the Sparse-Grid Gauss–Hermite Rule in Gaussian Sobolev Spaces 高斯Sobolev空间中拟蒙特卡罗方法的最优性和稀疏网格高斯- hermite规则的次最优性

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-10-16 DOI: 10.1137/25m1794346

Yoshihito Kazashi, Yuya Suzuki, Takashi Goda

引用次数: 0

Finite Element Error Analysis for Elliptic Parameter Identification with Power-Type Nonlinearity 幂型非线性椭圆参数辨识的有限元误差分析

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-10-16 DOI: 10.1137/26m1842646

De-Han Chen, Yi-Hsuan Lin, Irwin Yousept

{"title":"Finite Element Error Analysis for Elliptic Parameter Identification with Power-Type Nonlinearity","authors":"De-Han Chen, Yi-Hsuan Lin, Irwin Yousept","doi":"10.1137/26m1842646","DOIUrl":"https://doi.org/10.1137/26m1842646","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 5, Page 2151-2176, October 2026. Abstract. This paper studies the numerical analysis of a parameter identification problem governed by elliptic equations with power-type nonlinearity. We propose a numerical reconstruction via a suitable least-squares minimization problem based on piecewise linear finite elements. As one of our main novelties, we establish conditional stability estimates at the continuous level, which form the theoretical foundation of the present finite element analysis. Our stability analysis relies on tailored analytical tools, including Hardy-type inequalities, fractional Gagliardo–Nirenberg inequalities, and weighted spaces with singular distance weights. By invoking the achieved conditional stability together with the Carstensen quasi-interpolation operator and associated estimates in negative Sobolev spaces, we derive a priori error estimates for the proposed finite element approximation in terms of the mesh size, the regularization parameter, the noise level, and the nonlinearity exponent. Our results extend the recent stability and error estimates for the linear case by Jin et al. [] and sharpen their error estimates and convergence order under weaker regularity assumptions.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"13 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149187909","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

Density Estimation via Periodic Scaled Korobov Kernel Method with Exponential Decay Condition 基于指数衰减条件的周期尺度Korobov核密度估计

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-10-12 DOI: 10.1137/25m1770370

Ziyang Ye, Haoyuan Tan, Xiaoqun Wang, Zhijian He

{"title":"Density Estimation via Periodic Scaled Korobov Kernel Method with Exponential Decay Condition","authors":"Ziyang Ye, Haoyuan Tan, Xiaoqun Wang, Zhijian He","doi":"10.1137/25m1770370","DOIUrl":"https://doi.org/10.1137/25m1770370","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 5, Page 2100-2122, October 2026. Abstract. We propose the periodic scaled Korobov kernel (PSKK) method for nonparametric density estimation on [math]. By first wrapping the target density into a periodic version through modulo operation and subsequently applying kernel ridge regression in scaled Korobov spaces, we extend the kernel approach proposed by Kazashi and Nobile [SIAM J. Numer. Anal., 61 (2023), pp. 1080–1102] and eliminate its requirement for inherent periodicity of the density function. This key modification enables effective estimation of densities defined on unbounded domains. We establish rigorous mean integrated squared error (MISE) bounds, proving that for densities with smoothness of order [math] and exponential decay, our PSKK method achieves an [math] MISE convergence rate with an arbitrarily small [math]. While matching the convergence rate of the previous kernel approach, our method applies to nonperiodic distributions at the cost of stronger differentiability and exponential decay assumptions. Numerical experiments confirm the theoretical results and demonstrate a significant improvement over traditional kernel density estimation in large-sample regimes.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"33 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149152577","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

A Dichotomy of Finite Element Spaces and Its Application to an Energy-Conservative Scheme for the Regularized Long Wave Equation 有限元空间的二分法及其在正则长波方程能量守恒格式中的应用

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-09-24 DOI: 10.1137/25m1834740

Dimitrios Antonopoulos, Dimitrios Mitsotakis

{"title":"A Dichotomy of Finite Element Spaces and Its Application to an Energy-Conservative Scheme for the Regularized Long Wave Equation","authors":"Dimitrios Antonopoulos, Dimitrios Mitsotakis","doi":"10.1137/25m1834740","DOIUrl":"https://doi.org/10.1137/25m1834740","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 5, Page 2079-2099, October 2026. Abstract. Certain energy-conservative Galerkin discretizations for nonlinear dispersive wave equations have revealed an unusual convergence behavior: optimal convergence is attained when continuous Lagrange finite element spaces of odd polynomial degree are employed, whereas the use of even-degree polynomials leads to reduced convergence rate. The present work demonstrates that this behavior is intrinsic to the structure of the finite element spaces themselves. In particular, it is shown to be closely connected to the standard [math]-projection of derivatives, which possesses a super-approximation property exclusively for odd polynomial degrees. We also examine the implications of this feature for an energy-conservative Galerkin approximation of the regularized long-wave equation where the energy is a cubic functional. Although the resulting scheme conserves both mass and energy, we further show that the impulse is approximated with high accuracy, and we establish a priori error bounds for the associated semidiscrete formulation.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"30 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149043592","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

An ({hp})-Version Time Stepping Spectral Monte Carlo Method for Semi-linear Parabolic Equations 一个半线性抛物方程的时间步进谱蒙特卡罗方法({hp}) -版本

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-09-22 DOI: 10.1137/25m1787045

Jiaying Feng, Zhiyuan Hui, Changtao Sheng, Chenglong Xu

{"title":"An ({hp})-Version Time Stepping Spectral Monte Carlo Method for Semi-linear Parabolic Equations","authors":"Jiaying Feng, Zhiyuan Hui, Changtao Sheng, Chenglong Xu","doi":"10.1137/25m1787045","DOIUrl":"https://doi.org/10.1137/25m1787045","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 5, Page 2051-2078, October 2026. Abstract. In this paper, we present an [math]-version time-stepping spectral Monte Carlo method for solving semilinear parabolic equations. The key innovation lies in constructing an exponentially accurate stochastic algorithm that integrates a residual iteration scheme on Gauss-type nodes in both temporal and spatial directions with a reconstruction strategy rooted in spectral methods. To address the long-time simulations and initial singularities that are often challenging for traditional stochastic algorithms (e.g., walk-on-spheres method), we further develop an [math]-version time-stepping framework that employs multiple time steps and, respectively, geometric time partitions with linearly increasing polynomial degrees to handle these difficulties. Notably, the proposed algorithm bypasses the need to solve linear systems required by traditional spectral methods and remarkably supports parallel computation at both temporal and spatial grid points. We rigorously establish exponential convergence rates for the multistep method within a finite number of iterations. Extensive numerical experiments are conducted to demonstrate the spectral accuracy and computational efficiency of the proposed method in long-time simulations, problems with initial singularities, and a five-dimensional problem, thereby validating the theoretical results.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"54 1","pages":"2051-2078"},"PeriodicalIF":2.9,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149021147","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

Convergence of Explicit Runge–Kutta Discontinuous Galerkin Approximations of the First-Order Form of Maxwell’s Equations with Low Regularity Solutions 具有低正则解的Maxwell方程组一阶形式的显式Runge-Kutta不连续Galerkin逼近的收敛性

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-09-22 DOI: 10.1137/25m1774793

Alexandre Ern, Jean-Luc Guermond

{"title":"Convergence of Explicit Runge–Kutta Discontinuous Galerkin Approximations of the First-Order Form of Maxwell’s Equations with Low Regularity Solutions","authors":"Alexandre Ern, Jean-Luc Guermond","doi":"10.1137/25m1774793","DOIUrl":"https://doi.org/10.1137/25m1774793","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 5, Page 2028-2050, October 2026. Abstract. We establish a convergence result for the approximation of low-regularity solutions to time-dependent PDE systems that have an involution structure similar to Maxwell’s equations and the linear wave equations. The approximation is based on an explicit Runge–Kutta (ERK) time-stepping and the discontinuous Galerkin (dG) method with stabilization (so-called upwind fluxes) in space. The regularity setting only assumes that the exact solution and its first time derivative are in [math] with a Sobolev regularity index [math] in [math] (here, [math] is the time interval and [math] the space domain), and that its second time derivative is in [math]. The two main tools for the convergence analysis are a Ritz projection in space that leverages recent convergence results in operator norm for the dG approximation of the steady form of the PDE, and the [math]-stability under a standard CFL condition of three-stage, third-order and four-stage, fourth-order ERK schemes. These latter results are known in the literature, but we provide here a somewhat simpler argument to prove the [math]-stability.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"2 1","pages":"2028-2050"},"PeriodicalIF":2.9,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149021148","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

Monte Carlo Quasi-Interpolation of Spherical Data 球面数据的蒙特卡罗拟插值

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-09-21 DOI: 10.1137/25m1810490

Zhengjie Sun, Mengyuan Lv, Xingping Sun

引用次数: 0

A Unified Framework for the Analysis, Numerical Approximation, and Model Reduction of Linear Operator Equations, Part I: Well-Posedness in Space and Time 线性算子方程的分析、数值近似和模型简化的统一框架，第一部分：空间和时间的适定性

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-09-18 DOI: 10.1137/25m1786040

Moritz Feuerle, Richard Löscher, Olaf Steinbach, Karsten Urban

引用次数: 0

Analysis of a Schwarz–Fourier Domain Decomposition Method Schwarz-Fourier域分解方法的分析

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-09-11 DOI: 10.1137/25m1818369

Arnold Reusken

引用次数: 0

A Convergence Framework for Energy Minimization of Linear Self-Adjoint Elliptic PDEs in Nonlinear Approximation Spaces 非线性逼近空间中线性自伴随椭圆偏微分方程能量最小化的收敛框架

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-09-10 DOI: 10.1137/25m1791470

Alexandre Magueresse, Santiago Badia

{"title":"A Convergence Framework for Energy Minimization of Linear Self-Adjoint Elliptic PDEs in Nonlinear Approximation Spaces","authors":"Alexandre Magueresse, Santiago Badia","doi":"10.1137/25m1791470","DOIUrl":"https://doi.org/10.1137/25m1791470","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 5, Page 1923-1957, October 2026. Abstract. Recent years have seen growing interest in solving partial differential equations (PDEs) using nonlinear approximation spaces, where tunable parameters control the basis functions and allow the discretization to adapt dynamically to the solution. While these approaches often perform well in practice, convergence guarantees for the underlying optimization problem remain scarce. This work develops a general optimization framework for energy minimization problems arising from linear self-adjoint elliptic PDEs, formulated over nonlinear approximation spaces admitting a natural split between linear and nonlinear parameters. Linear variables are updated via linear solves or steepest descent, while nonlinear variables are handled using projected gradient descent. We establish local convergence in gradients and in values under modular structural assumptions, including differentiability, boundedness, regularity, and directional convexity, and provide explicit convergence rates in terms of the structural constants of the problem. These assumptions are verified for a broad class of nonlinear approximation spaces, including adaptive finite elements, free-knot splines, kernel methods, and weight-constrained neural networks. Numerical experiments illustrate the benefits of the parameter split and several key aspects of the framework. In a recent work [Magueresse, Badia (2025, arXiv:2508.17705)], we apply the framework to overlapping free-knot tensor-product B-splines, obtaining a geometrically adaptive solver with rigorous convergence guarantees.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"16 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148915612","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