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On the superconvergence of a WG method for the elliptic problem with variable coefficients
《Science China Mathematics》2024年第8期1899-1910,共12页Junping Wang Xiaoshen Wang Xiu Ye Shangyou Zhang Peng Zhu 
supported by U.S.National Science Foundation IR/D program while working at U.S.National Science Foundation;supported by U.S.National Science Foundation(Grant No.DMS-1620016);supported by Zhejiang Provincial Natural Science Foundation of China(Grant No.LY23A010005);National Natural Science Foundation of China(Grant No.12071184)。
This article extends a recently developed superconvergence result for weak Galerkin(WG)approximations for modeling partial differential equations from constant coefficients to variable coefficients.This superconvergen...
关键词：weak Galerkin finite element methods SUPERCONVERGENCE second-order elliptic problems stabilizerfree 
Second-order error analysis of the averaged L1 scheme L1 for time-fractional initial-value and subdiffusion problems
《Science China Mathematics》2024年第7期1641-1664,共24页Jinye Shen Fanhai Zeng Martin Stynes 
supported by National Natural Science Foundation of China (Grant Nos. 12101509, 12171283, 12171025 and NSAF-U1930402);the Science Foundation Program for Distinguished Young Scholars of Shandong (Overseas) (Grant No. 2022HWYQ-045)。
Fractional initial-value problems(IVPs) and time-fractional initial-boundary value problems(IBVPs), each with a Caputo temporal derivative of order α ∈(0, 1), are considered. An averaged variant of the well-known L1...
关键词：time-fractional SUBDIFFUSION averaged L1 scheme 
Data-driven slicing for dimension reduction in regressions:A likelihood-ratio approach
《Science China Mathematics》2024年第3期647-664,共18页Peirong Xu Tao Wang Lixing Zhu 
supported by National Natural Science Foundation of China(Grant Nos.11971017 and 11971018);Shanghai Rising-Star Program(Grant No.20QA1407500);Multidisciplinary Cross Research Foundation of Shanghai Jiao Tong University(Grant Nos.YG2019QNA26,YG2019QNA37 and YG2021QN06);Neil Shen's SJTU Medical Research Fund of Shanghai Jiao Tong University。
To efficiently estimate the central subspace in sufficient dimension reduction,response discretization via slicing its range is one of the most used methodologies when inverse regression-based methods are applied.Howe...
关键词：full-likelihood approach adaptive slicing REGULARIZATION second-order method 
Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation
《Science China Mathematics》2024年第1期187-210,共24页Xiao Li Zhonghua Qiao Cheng Wang 
supported by the Chinese Academy of Sciences(CAS)Academy of Mathematics and Systems Science(AMSS);the Hong Kong Polytechnic University(PolyU)Joint Laboratory of Applied Mathematics;supported by the Hong Kong Research Council General Research Fund(Grant No.15300821);the Hong Kong Polytechnic University Grants(Grant Nos.1-BD8N,4-ZZMK and 1-ZVWW);supported by the Hong Kong Research Council Research Fellow Scheme(Grant No.RFS2021-5S03);General Research Fund(Grant No.15302919);supported by US National Science Foundation(Grant No.DMS-2012269)。
In this paper,we study a second-order accurate and linear numerical scheme for the nonlocal CahnHilliard equation.The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth ...
关键词：nonlocal Cahn-Hilliard equation second-order stabilized scheme higher-order consistency analysis rough and refined error estimate 
Normalized solutions for a fourth-order Schrődinger equation with a positive second-order dispersion coefficient
《Science China Mathematics》2023年第6期1237-1262,共26页Xiao Luo Tao Yang 
supported by National Natural Science Foundation of China (Grant No.11901147);the Fundamental Research Funds for the Central Universities of China (Grant No.JZ2020HGTB0030)。
In this paper,we study normalized solutions to a fourth-order Schrődinger equation with a positive second-order dispersion coefficient in the mass supercritical regime.Unlike the well-studied case where the second-ord...
关键词：fourth-order Schrodinger equation mixed dispersion normalized solution variational method 
Unified convergence analysis of a second-order method of multipliers for nonlinear conic programming
《Science China Mathematics》2022年第11期2397-2422,共26页Liang Chen Junyuan Zhu Xinyuan Zhao 
supported by National Natural Science Foundation of China (Grant No. 11801158);the Hunan Provincial Natural Science Foundation of China (Grant No. 2019JJ50040);the Fundamental Research Funds for the Central Universities in China;supported by National Natural Science Foundation of China (Grant No. 11871002);the General Program of Science and Technology of Beijing Municipal Education Commission (Grant No. KM201810005004)
In this paper,we accomplish the unified convergence analysis of a second-order method of multipliers(i.e.,a second-order augmented Lagrangian method)for solving the conventional nonlinear conic optimization problems.S...
关键词：second-order method of multipliers augmented Lagrangian method convergence rate generalized Newton method second-order cone programming semidefinite programming 
On the local convergence of a stochastic semismooth Newton method for nonsmooth nonconvex optimization被引量：1
《Science China Mathematics》2022年第10期2151-2170,共20页Andre Milzarek Xiantao Xiao Zaiwen Wen Michael Ulbrich 
supported by the Fundamental Research Fund—Shenzhen Research Institute for Big Data Startup Fund(Grant No.JCYJ-AM20190601);the Shenzhen Institute of Artificial Intelligence and Robotics for Society;National Natural Science Foundation of China(Grant Nos.11831002 and 11871135);the Key-Area Research and Development Program of Guangdong Province(Grant No.2019B121204008);Beijing Academy of Artificial Intelligence。
In this work,we present probabilistic local convergence results for a stochastic semismooth Newton method for a class of stochastic composite optimization problems involving the sum of smooth nonconvex and nonsmooth c...
关键词：nonsmooth stochastic optimization stochastic approximation semismooth Newton method stochastic second-order information local convergence 
Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection被引量：4
《Science China Mathematics》2021年第5期887-902,共16页Hong-Lin Liao Xuehua Song Tao Tang Tao Zhou 
supported by National Natural Science Foundation of China(Grant No.12071216);supported by National Natural Science Foundation of China(Grant No.11731006);the NNW2018-ZT4A06 project;supported by National Natural Science Foundation of China(Grant Nos.11822111,11688101 and 11731006);the Science Challenge Project(Grant No.TZ2018001)。
In this work,we are concerned with the stability and convergence analysis of the second-order backward difference formula(BDF2)with variable steps for the molecular beam epitaxial model without slope selection.We firs...
关键词：molecular beam epitaxial growth variable-step BDF2 scheme discrete orthogonal convolution kernels energy stability convergence analysis 
L^p-gradient estimates for the commutators of the Kato square roots of second-order elliptic operators on R^n
《Science China Mathematics》2020年第3期575-594,共20页Wenyu Tao Yanping Chen Yayuan Xiao Liwei Wang 
supported by National Natural Science Foundation of China (Grant No. 11471033);Program for New Century Excellent Talents in University of China (Grant No. NCET-11-0574);the Fundamental Research Funds for the Central Universities (Grant No. FRF-BR-17-001B);the Fundamental Research Funds for Doctoral Candidate of University of Science and Technology Beijing (Grant No. FRF-BR-17018)
Let L=-div（A▽） be a second-order divergent-form elliptic operator,where A is an accretive n×n matrix with bounded and measurable complex coefficients on Herein,we prove that the commutator [b,L1/2]of the Kato squa...
关键词：COMMUTATOR Kato square root elliptic operators Sobolev space 
Optimality conditions for sparse nonlinear programming被引量：8
《Science China Mathematics》2017年第5期759-776,共18页PAN LiLi XIU NaiHua FAN Jun 
supported by National Natural Science Foundation of China(Grant No.11431002);Shandong Province Natural Science Foundation(Grant No.ZR2016AM07)
The sparse nonlinear programming （SNP） is to minimize a general continuously differentiable func- tion subject to sparsity, nonlinear equality and inequality constraints. We first define two restricted constraint qu...
关键词：sparse nonlinear programming constraint qualification normal cone first-order optimality con-dition second-order optimality condition 
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