SIAM Journal on Numerical Analysis最新文献

Superconvergent and Divergence-Free Mixed Finite Element Methods for the Stokes Equation Stokes方程的超收敛无发散混合有限元方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-09-04 DOI: 10.1137/25m1812087

Long Chen, Xuehai Huang, Chao Zhang, Xinyue Zhao

{"title":"Superconvergent and Divergence-Free Mixed Finite Element Methods for the Stokes Equation","authors":"Long Chen, Xuehai Huang, Chao Zhang, Xinyue Zhao","doi":"10.1137/25m1812087","DOIUrl":"https://doi.org/10.1137/25m1812087","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 5, Page 1831-1860, October 2026. <br/> Abstract. This paper develops divergence-free mixed finite element methods for the Stokes equation. Using H(div)-conforming velocities and discontinuous pressures ensures the inf-sup condition for the velocity–pressure pair and yields pointwise divergence-free velocities. However, this choice makes the vector Laplacian difficult to discretize. Inspired by mass-conserving mixed formulations with stresses, tangential–normal continuous traceless tensor elements are used to discretize the vector Laplacian. An inf-sup condition for the weak div operator between the stress and velocity spaces is then proved. Two key properties characterize the scheme. First, the stress–velocity inf-sup stability gives a stable discretization of the vector Laplacian without additional stabilization, unlike discontinuous Galerkin or virtual element methods. Second, the scheme has the property that if a stress field is distributionally divergence-free against the discrete divergence-free velocity space, then it is also distributionally divergence-free against the continuous divergence-free velocity space. This property decouples the stress and velocity errors and leads to superconvergence. As a result, optimal-order error estimates are obtained for the stress, while the discrete velocity is superclose to its H(div) interpolant. The projected-pressure error estimate is optimal with Raviart-Thomas velocities and superconvergent with Brezzi-Douglas-Marini velocities, while local postprocessing yields an elementwise divergence-free velocity with higher-order convergence[math]. Numerical experiments confirm the theoretical results.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"28 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148890197","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

Finite Element Analysis of a Nematic Liquid Crystal Landau–de Gennes Model with Quartic Elastic Terms 具有四次弹性项的向列液晶Landau-de Gennes模型的有限元分析

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-09-01 DOI: 10.1137/24m1694203

Jacob Elafandi, Franziska Weber

引用次数: 0

A Hybrid High-Order Method for the Power-Law Brinkman Problem with Robust Error Estimates in all Regimes 具有鲁棒误差估计的幂律Brinkman问题的混合高阶方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-08-24 DOI: 10.1137/25m1778389

D. Castañón Quiroz, D. A. Di Pietro, J. Droniou, M. Salah

引用次数: 0

Error Formulas for Block Rational Krylov Approximations of Matrix Functions 矩阵函数块有理Krylov近似的误差公式

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-08-20 DOI: 10.1137/25m1751815

Stefano Massei, Leonardo Robol

引用次数: 0

A Posteriori Error Estimates for Parabolic Partial Differential Equations on Stationary Surfaces 平稳曲面上抛物型偏微分方程的后验误差估计

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-08-17 DOI: 10.1137/25m1784466

Balázs Kovács, Michael Lantelme

引用次数: 0

Error Estimates of an Exponential Wave Integrator for the Nonlinear Schrödinger Equation with Singular Potential 具有奇异势的非线性Schrödinger方程的指数波积分器误差估计

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-08-13 DOI: 10.1137/25m1748317

Weizhu Bao, Chushan Wang

{"title":"Error Estimates of an Exponential Wave Integrator for the Nonlinear Schrödinger Equation with Singular Potential","authors":"Weizhu Bao, Chushan Wang","doi":"10.1137/25m1748317","DOIUrl":"https://doi.org/10.1137/25m1748317","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 4, Page 1682-1704, August 2026. <br/> Abstract. In this paper we analyze a first-order exponential wave integrator (EWI) for the nonlinear Schrödinger equation (NLSE) with a singular potential that is locally in [math], which might be locally unbounded. A typical example is the inverse power potential such as the Coulomb potential, which is the most fundamental potential in quantum physics and chemistry. We prove that, under the assumption of [math]-potential and [math]-initial data, the [math]-norm convergence of the EWI is, roughly, first-order in one dimension (1D) and two dimensions (2D), and [math]-order in three dimensions (3D). In addition, under a stronger integrability assumption of [math]-potential for some [math] in 3D, the [math]-norm convergence increases to almost [math]-order if [math] and becomes first-order if [math]. In particular, our results show, to the best of our knowledge for the first time, that first-order [math]-norm convergence can be achieved when solving the NLSE with the Coulomb potential in 3D. The key advancements are the use of discrete (in time) Strichartz estimates, which allow us to handle the loss of integrability due to the singular potential that does not belong to [math], and the more favorable local truncation error of the EWI, which requires no (spatial) smoothness of the potential. Extensive numerical results in 1D, 2D, and 3D are reported to confirm our error estimates and to show the sharpness of our assumptions on the regularity of the singular potentials.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"42 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148717842","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

Mixed FEM for Coupled Unsteady Fluid Flow Problems with [math]-Type Brinkman–Forchheimer Framework and its Application for Reverse-Osmosis Desalination [数学]型Brinkman-Forchheimer框架耦合非定常流体流动问题的混合有限元法及其在反渗透海水淡化中的应用

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-08-12 DOI: 10.1137/25m1767650

Zeinab Gharibi, Mostafa Abbaszadeh, Mehdi Dehghan

{"title":"Mixed FEM for Coupled Unsteady Fluid Flow Problems with [math]-Type Brinkman–Forchheimer Framework and its Application for Reverse-Osmosis Desalination","authors":"Zeinab Gharibi, Mostafa Abbaszadeh, Mehdi Dehghan","doi":"10.1137/25m1767650","DOIUrl":"https://doi.org/10.1137/25m1767650","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 4, Page 1645-1681, August 2026. <br/> Abstract. This work analyzes a fully discrete mixed finite element method in a Banach space framework for solving nonstationary coupled fluid flow problems modeled by the Brinkman–Forchheimer equations, with applications to reverse osmosis. The model couples unsteady [math]-type convective Brinkman–Forchheimer and transport equations with nonlinear boundary conditions across a semipermeable membrane. A mixed formulation is used for both the fluid equation (pseudostress-velocity) and the transport equation (concentration, its gradient, and a Lagrange multiplier from the membrane condition). The continuous problem is reformulated in Banach spaces as a fixed-point problem, enabling a well-posedness analysis via differential-algebraic system theory. Spatial discretization employs lowest-order Raviart–Thomas elements for fluxes and piecewise constants for primal variables, while linear elements are used for the Lagrange multiplier. A fully discrete Galerkin scheme with backward Euler time-stepping is proposed. Its well-posedness and stability are proven using a fixed-point argument, and optimal convergence rates are established. Numerical results confirm the theoretical error estimates and demonstrate the method’s effectiveness.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"29 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148728086","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 Surface Finite Element Scheme for a Stochastic PDE on an Evolving Curve 演化曲线上随机偏微分方程的曲面有限元格式

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-08-11 DOI: 10.1137/25m1774173

Paola Pozzi, Björn Stinner

引用次数: 0

Robust Stability and Preconditioning of Darcy–Forchheimer Equations Darcy-Forchheimer方程的鲁棒稳定性与预处理

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-08-11 DOI: 10.1137/25m1816115

Rishi Das, Harsha Hutridurga, Amiya K. Pani, Ricardo Ruiz-Baier

引用次数: 0

Theory and Internal Structure of ADER-DG Method for Ordinary Differential Equations 常微分方程的ADER-DG方法的理论和内部结构