FINITE_ELEMENT

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NUMERICAL ANALYSIS FOR STOCHASTIC TIME-SPACE FRACTIONAL DIFFUSION EQUATION DRIVEN BY FRACTIONAL GAUSSIAN NOISE
《Journal of Computational Mathematics》2024年第6期1502-1525,共24页Daxin Nie Weihua Deng 
supported by the National Natural Science Foundation of China(Grant Nos.12071195,12301509,12225107);by the Innovative Groups of Basic Research in Gansu Province(Grant No.22JR5RA391);by the Major Science and Technology Projects in Gansu Province-Leading Talents in Science and Technology(Grant No.23ZDKA0005);by the Science and Technology Plan of Gansu Province(Grant No.22JR5RA535);by the Fundamental Research Funds for the Central Universities(Grant No.lzujbky-2023-pd04);by the China Postdoctoral Science Foundation(Grant No.2023M731466).
In this paper,we consider the strong convergence of the time-space fractional diffusion equation driven by fractional Gaussian noise with Hurst index H∈(1/2,1).A sharp regularity estimate of the mild solution and the...
关键词：Fractional Laplacian Stochastic fractional diffusion equation Fractional Gaussian noise Finite element Convolution quadrature Error analysis 
A COUPLED METHOD COMBINING CROUZEIX-RAVIART NONCONFORMING AND NODE CONFORMING FINITE ELEMENT SPACES FOR BOIT CONSOLIDATION MODEL
《Journal of Computational Mathematics》2024年第4期911-931,共21页Yuping Zeng Mingchao Cai Liuqiang Zhong 
supported by the Guangdong Basic and Applied Basic Research Foundation(Grant No.2020A1515011032);The work of M.Cai is supported in part by the NIH-BUILD(Grant No.UL1GM118973);by the NIH-RCMI(Grant No.U54MD013376);the National Science Foundation awards(Grant Nos.1700328,1831950);The work of L.Zhong is supported by the National Natural Science Foundation of China(Grant No.12071160)。
A mixed finite element method is presented for the Biot consolidation problem in poroe-lasticity.More precisely,the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements,while the fu...
关键词：Poroelasticity Nonconforming finite element Inf-sup condition A priori error estimate 
TWO-GRID FINITE ELEMENT METHOD FOR TIME-FRACTIONAL NONLINEAR SCHRODINGER EQUATION
《Journal of Computational Mathematics》2024年第4期1124-1144,共21页Hanzhang Hu Yanping Chen Jianwei Zhou 
supported by the State Key Program of National Natural Science Foundation of China(Grant No.11931003);by the National Natural Science Foundation of China(Grant Nos.41974133,12271233);The work of first author was supported by the Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2024A1515012430,2020A1515011032);by the Educational Commission of Guangdong Province,China(Grant No.2019KTSCX174).
A two-grid finite element method with L1 scheme is presented for solving two-dimen-sional time-fractional nonlinear Schrodinger equation.The finite element solution in the L-norm are proved bounded without any time-st...
关键词：Time-fractional nonlinear Schrodinger equation Two-grid finite element me-thod The L1 scheme 
CONVERGENCE ANALYSIS OF SOME FINITE ELEMENT PARALLEL ALGORITHMS FOR THE STATIONARY INCOMPRESSIBLE MHD EQUATIONS
《Journal of Computational Mathematics》2024年第1期49-70,共22页Xiaojing Dong Yinnian He 
supported by the National Natural Science Foundation of China(Grant Nos.12071404,12271465,12026254);by the Young Elite Scientist Sponsorship Program by CAST(Grant No.2020QNRC001);by the China Postdoctoral Science Foundation(Grant No.2018T110073);by the Natural Science Foundation of Hunan Province(Grant No.2019JJ40279);by the Excellent Youth Program of Scientific Research Project of Hunan Provincial Department of Education(Grant No.20B564);by the International Scientific and Technological Innovation Cooperation Base of Hunan Province for Computational Science(Grant No.2018WK4006).
By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are pre...
关键词：Partition of unity method Local and parallel algorithm Finite element method Iteration methods MAGNETOHYDRODYNAMICS 
A NEW FINITE ELEMENT SPACE FOR EXPANDED MIXED FINITE ELEMENT METHOD
《Journal of Computational Mathematics》2023年第5期817-840,共24页Jing Chen Zhaojie Zhou Huanzhen Chen Hong Wang 
supported by NSF of China grant 11971276;H.Chen was supported by NSF of China grants 12171287,10971254 and 11471196;H.Wang was supported by the ARO MURI Grant W911NF-15-1-0562;by the National Science Foundation under Grant DMS-2012291.
In this article,we propose a new finite element spaceΛh for the expanded mixed finite element method(EMFEM)for second-order elliptic problems to guarantee its computing capability and reduce the computation cost.The ...
关键词：New finite element space Expanded mixed finite element Minimum degrees of freedom The inf-sup condition SOLVABILITY Optimal convergence. 
GRADIENT FLOW FINITE ELEMENT DISCRETISATIONS WITH ENERGY-BASED ADAPTIVITY FOR EXCITED STATES OF SCHRÖDINGER'S EQUATION
《Journal of Computational Mathematics》2023年第5期933-955,共23页Pascal Heid 
the financial support of the Swiss National Science Foundation(SNSF),Project No.P2BEP2_191760.
The purpose of this paper is to verify that the computational scheme from[Heid et al.,Gradient flow finite element discretizations with energy-based adaptivity for the Gross–Pitaevskii equation,J.Comput.Phys.436(2021...
关键词：Schrodinger’s equation Excited states Gradient flows Adaptive finite element methods 
ON FINITE ELEMENT APPROXIMATIONS TO A SHAPE GRADIENT FLOW IN SHAPE OPTIMIZATION OF ELLIPTIC PROBLEMS
《Journal of Computational Mathematics》2023年第5期956-979,共24页Chunxiao Liu Shengfeng Zhu 
supported in part by the National Key Basic Research Program under grant 2022YFA1004402;the Science and Technology Commission of Shanghai Municipality(Nos.21JC1402500,22ZR1421900,and 22DZ2229014);the National Natural Science Foundation of China under grant(No.12071149).
Shape gradient flows are widely used in numerical shape optimization algorithms.We investigate the accuracy and effectiveness of approximate shape gradients flows for shape optimization of elliptic problems.We present...
关键词：Shape optimization Shape gradient Eulerian derivative Finite element Error estimate 
A PRIORI ERROR ESTIMATES FOR OBSTACLE OPTIMAL CONTROL PROBLEM,WHERE THE OBSTACLE IS THE CONTROLITSELF
《Journal of Computational Mathematics》2023年第4期717-740,共24页Yazid Dendani Radouen Ghanem 
In this paper we deal with the convergence analysis of the finite element method for an elliptic penalized unilateral obstacle optimal control problem where the control and the obstacle coincide.Error estimates are es...
关键词：Optimal control Obstacle problem Finite element A priori error estimate 
ANALYSIS OF A MULTI-TERM VARIABLE-ORDER TIME-FRACTIONAL DIFFUSION EQUATION AND ITS GALERKIN FINITE ELEMENT APPROXIMATION
《Journal of Computational Mathematics》2022年第5期814-834,共21页Huan Liu Xiangcheng Zheng Hongfei Fu 
the National Natural Science Foundation of China(No.11971482);the Natural Science Foundation of Shandong Province(No.ZR2017MA006);the National Science Foundation(No.DMS-1620194);the China Postdoctoral Science Foundation(Nos.2020M681136,2021TQ0017,2021T140129);the International Postdoctoral Exchange Fellowship Program(Talent-Introduction Program)(No.YJ20210019).
In this paper,we study the well-posedness and solution regularity of a multi-term variable-order time-fractional diffusion equation,and then develop an optimal Galerkin finite element scheme without any regularity ass...
关键词：Variable-order Multi-term time-fractional diffusion equation Solution regularity Galerkin finite element Parareal method. 
A FINITE ELEMENT ALGORITHM FOR NEMATIC LIQUID CRYSTAL FLOW BASED ON THE GAUGE-UZAWA METHOD
《Journal of Computational Mathematics》2022年第1期26-43,共18页Pengzhan Huang Yinnian He Ting Li 
supported by the Natural Science Foundation of China(grant number 11861067).
In this paper,we present a finite element algorithm for the time-dependent nematic liquid crystal flow based on the Gauge-Uzawa method.This algorithm combines the Gauge and Uzawa methods within a finite element variat...
关键词：Nematic liquid crystal model Finite element approximation Gauge-Uzawa method Error analysis 
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