SIAM Journal on Numerical Analysis最新文献

Wasserstein Convergence Rates for Stochastic Particle Approximation of Boltzmann Models Boltzmann模型随机粒子逼近的Wasserstein收敛速率

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-04-10 DOI: 10.1137/25m1751347

Giacomo Borghi, Lorenzo Pareschi

引用次数: 0

Analysis of BDDC Preconditioners for Nonconforming Polytopal Hybrid Discretization Methods 不合格多拓扑混合离散化方法的BDDC预调节器分析

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-04-09 DOI: 10.1137/25m1768801

Santiago Badia, Jerome Droniou, Jordi Manyer, Jai Tushar

{"title":"Analysis of BDDC Preconditioners for Nonconforming Polytopal Hybrid Discretization Methods","authors":"Santiago Badia, Jerome Droniou, Jordi Manyer, Jai Tushar","doi":"10.1137/25m1768801","DOIUrl":"https://doi.org/10.1137/25m1768801","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 2, Page 456-484, April 2026. Abstract. In this work, we build on the discrete trace theory developed by Badia, Droniou, and Tushar (Foundations of Computational Mathematics, in press, 2025; doi:10.1007/s10208-025-09734-6) to analyze the convergence rate of the balancing domain decomposition by constraints (BDDC) preconditioner generated from nonconforming polytopal hybrid discretizations. We prove polylogarithmic bounds on the condition number for the preconditioner that are independent of the mesh parameter and the number of subdomains and that hold on polytopal meshes. The analysis relies on the continuity of a face truncation operator, which we establish in the fully discrete polytopal setting. To validate the theory, we present numerical experiments that confirm the truncation estimate and condition number bounds. In particular, we conduct weak scalability tests for second-order elliptic problems discretized using discontinuous skeletal methods, specifically hybridizable discontinuous Galerkin and hybrid high-order methods. We also demonstrate the robustness of the preconditioner for piecewise discontinuous coefficients with large jumps.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"33 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642116","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

Multipoint Stress Mixed Finite Element Methods for Elasticity on Cuboid Grids 长方体网格弹性的多点应力混合有限元法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-04-07 DOI: 10.1137/25m1730752

Ibrahim Yazici, Ivan Yotov

{"title":"Multipoint Stress Mixed Finite Element Methods for Elasticity on Cuboid Grids","authors":"Ibrahim Yazici, Ivan Yotov","doi":"10.1137/25m1730752","DOIUrl":"https://doi.org/10.1137/25m1730752","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 2, Page 430-455, April 2026. Abstract. We develop multipoint stress mixed finite element methods for linear elasticity with weak stress symmetry on cuboid grids, which can be reduced to a symmetric and positive definite cell-centered system. The methods employ the lowest-order enhanced Raviart–Thomas finite element space for the stress and piecewise constant displacement. The vertex quadrature rule is employed to localize the interaction of stress degrees of freedom, enabling local stress elimination around each vertex. We introduce two methods. The first method uses a piecewise constant rotation, resulting in a cell-centered system for the displacement and rotation. The second method employs a continuous piecewise trilinear rotation and the vertex quadrature rule for the asymmetry bilinear forms, allowing for further elimination of the rotation and resulting in a cell-centered system for the displacement only. Stability and error analysis are performed for both methods. For the stability analysis of the second method, a new auxiliary [math]-conforming matrix-valued space is constructed, which forms an exact sequence with the stress space. A matrix-matrix inf-sup condition is shown for the curl of this auxiliary space and the trilinear rotation space. First-order convergence is established for all variables in their natural norms, as well as second-order superconvergence of the displacement at the cell centers. Numerical results are presented to verify the theory.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"244 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147630620","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

Accuracy of the Ensemble Kalman Filter in the Near-Linear Setting 近线性环境下集合卡尔曼滤波的精度

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-03-17 DOI: 10.1137/25m1732544

E. Calvello, P. Monmarché, A. M. Stuart, U. Vaes

{"title":"Accuracy of the Ensemble Kalman Filter in the Near-Linear Setting","authors":"E. Calvello, P. Monmarché, A. M. Stuart, U. Vaes","doi":"10.1137/25m1732544","DOIUrl":"https://doi.org/10.1137/25m1732544","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 2, Page 391-429, April 2026. Abstract. The filtering distribution captures the statistics of the state of a possibly stochastic dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however, they behave poorly for high dimensional problems, suffering weight collapse. This issue is circumvented by the ensemble Kalman filter, which is an equal-weights interacting particle system. However, this finite particle system is only proven to approximate the true filter in the linear Gaussian case. In practice, however, it is applied in much broader settings; as a result, establishing its approximation properties more generally is important. There has been recent progress in the theoretical analysis of the algorithm in discrete time, establishing stability and error estimates, in relation to the true filter, in non-Gaussian settings; but the assumptions on the dynamics and observation models rule out the unbounded vector fields that arise in practice, and the analysis applies only to the mean field limit of the discrete time ensemble Kalman filter. The present work establishes error bounds between the filtering distribution and the finite particle discrete time ensemble Kalman filter when the dynamics and observation vector fields may be unbounded, allowing linear growth.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"12 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147478698","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

Local Time Integration for Friedrichs’ Systems Friedrichs系统的本地时间集成

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-03-09 DOI: 10.1137/25m1735627

Marlis Hochbruck, Malik Scheifinger

{"title":"Local Time Integration for Friedrichs’ Systems","authors":"Marlis Hochbruck, Malik Scheifinger","doi":"10.1137/25m1735627","DOIUrl":"https://doi.org/10.1137/25m1735627","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 2, Page 370-390, April 2026. Abstract. In this paper, we address the full discretization of Friedrichs’ systems with a two-field structure, such as Maxwell’s equations or the acoustic wave equation in div-grad form; cf. [W. Dörfler et al., Wave Phenomena: Mathematical Analysis and Numerical Approximation, Springer, Cham, 2023]. We focus on a discontinuous Galerkin space discretization applied to a locally refined mesh or a small region with high wave speed. This results in a stiff system of ordinary differential equations, where the stiffness is mainly caused by a small region of the spatial mesh. When using explicit time-integration schemes, the time stepsize is severely restricted by a few spatial elements, leading to a loss of efficiency. As a remedy, we propose and analyze a general leapfrog-based scheme which is motivated by [C. Carle and M. Hochbruck, SIAM J. Numer. Anal., 60 (2022), pp. 2897–2924]. The new, fully explicit, local time-integration method filters the stiff part of the system in such a way that its CFL condition is significantly weaker than that of the leapfrog scheme while its computational cost is only slightly larger. For this scheme, the filter function is a suitably scaled and shifted Chebyshev polynomial. While our main interest is in explicit local time-stepping schemes, the filter functions can be much more general, for instance, a certain rational function leads to the locally implicit method, proposed and analyzed in [M. Hochbruch and A. Sturm, SIAM J. Numer. Anal., 54 (2016), pp. 3167–3191]. Our analysis provides sufficient conditions on the filter function to ensure full order of convergence in space and second order in time for the whole class of local time-integration schemes.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"89 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147380646","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 Posteriori Error Control for Nonconvex Problems via Calibration 基于校正的非凸问题后验误差控制

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-03-04 DOI: 10.1137/25m1782959

Benjamin Berkels, Alexander Effland, Martin Rumpf, Jan Verhülsdonk

{"title":"A Posteriori Error Control for Nonconvex Problems via Calibration","authors":"Benjamin Berkels, Alexander Effland, Martin Rumpf, Jan Verhülsdonk","doi":"10.1137/25m1782959","DOIUrl":"https://doi.org/10.1137/25m1782959","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 2, Page 350-369, April 2026. Abstract. In this paper, a posteriori error estimates are derived for the approximation error of minimizers of functionals on the space of functions with bounded variation with a nonconvex lower-order term. To this end, the calibration method by Alberti, Bouchitté, and Dal Maso [Calc. Var. Partial Differential Equations, 16 (2003), pp. 299–333] allows the problem to be reformulated as a uniformly convex variational problem over characteristic functions of subgraphs in one dimension higher. A primal-dual approach is formulated where the duality of divergence and gradient properly incorporates boundary conditions for the primal variable. Based on this, a posteriori error estimates can be derived first for the relaxed problem in the [math]-norm. A cut-out argument allows converting this into an [math]-error estimate for the characteristic subgraph functions apart from the jump interface, whereas the area of the interfacial region is estimated separately. To apply the estimate, we consider as one possible discretization a conforming finite element space for the primal variable and a nonconforming space for the dual variable. Finally, we validate the a posteriori error estimates in numerical experiments for a prototypical nonconvex functional in one and two dimensions as well as depth estimation in stereo imaging, a classical computer vision problem.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"26 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147358813","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

Error Analysis of a Conforming Finite Element Method for the Modified Electromagnetic Transmission Eigenvalue Problem 修正电磁传输特征值问题的一致性有限元法误差分析

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-03-03 DOI: 10.1137/25m1723608

Jiayu Han, Jiguang Sun, Qian Zhang

{"title":"Error Analysis of a Conforming Finite Element Method for the Modified Electromagnetic Transmission Eigenvalue Problem","authors":"Jiayu Han, Jiguang Sun, Qian Zhang","doi":"10.1137/25m1723608","DOIUrl":"https://doi.org/10.1137/25m1723608","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 2, Page 303-325, April 2026. Abstract. The modified electromagnetic transmission eigenvalue problem (METEP) arises from the inverse scattering theory and can be used to detect changes of the material properties in nondestructive testing. This paper proposes and analyzes a conforming edge element method for the METEP. We establish a rigorous error analysis of the numerical eigenpairs by proving the uniform convergence of the discrete operator. In particular, as the problem contains two second order equations and is indefinite, we introduce auxiliary problems and show that they satisfy [math]-coercivity, based on which we prove the existence of both the continuous and discrete solution operators to the source problem. We then prove the uniform convergence of the discrete solution operator by reformulating the continuous and discrete solution operators. Optimal error estimates are obtained by investigating the adjoint problems and using the spectral approximation theory for compact operators. The theory is validated by numerical examples with various coefficients for different domains in both two and three dimensions.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147329709","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

Preasymptotic Error Estimates of Linear EEM and CIP-EEM for the Time-Harmonic Maxwell Equations with Large Wave Number 大波数时谐Maxwell方程线性EEM和CIP-EEM的预渐近误差估计

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-03-03 DOI: 10.1137/24m1680362

Shuaishuai Lu, Haijun Wu

引用次数: 0

Low-Rank Tensor Product Richardson Iteration for Radiative Transfer in Plane-Parallel Geometry 平面平行几何辐射传递的低秩张量积Richardson迭代

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-02-18 DOI: 10.1137/24m1648065

Markus Bachmayr, Riccardo Bardin, Matthias Schlottbom

{"title":"Low-Rank Tensor Product Richardson Iteration for Radiative Transfer in Plane-Parallel Geometry","authors":"Markus Bachmayr, Riccardo Bardin, Matthias Schlottbom","doi":"10.1137/24m1648065","DOIUrl":"https://doi.org/10.1137/24m1648065","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 1, Page 277-302, February 2026. Abstract. The radiative transfer equation (RTE) has been established as a fundamental tool for the description of energy transport, absorption, and scattering in many relevant societal applications and requires numerical approximations. However, classical numerical algorithms scale unfavorably with respect to the dimensionality of such radiative transfer problems, where solutions depend on physical as well as angular variables. In this paper, we address this dimensionality issue by developing a low-rank tensor product framework for the RTE in plane-parallel geometry. We exploit the tensor product nature of the phase space to recover an operator equation where the operator is given by a short sum of Kronecker products. This equation is solved by a preconditioned and rank-controlled Richardson iteration in Hilbert spaces. Using exponential sums approximations, we construct a preconditioner that is compatible with the low-rank tensor product framework. The use of suitable preconditioning techniques yields a transformation of the operator equation in Hilbert space into a sequence space with a Euclidean inner product, enabling rigorous error and rank control in the Euclidean metric.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"87 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146210246","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

Monotonicity and Convergence of Two-Relaxation-Times Lattice Boltzmann Schemes for a Nonlinear Conservation Law 一类非线性守恒律的双松弛次晶格Boltzmann格式的单调性和收敛性

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-02-06 DOI: 10.1137/25m1725218

Denise Aregba-Driollet, Thomas Bellotti

引用次数: 0