CONVERGENCE_ANALYSIS

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CONVERGENCE ANALYSIS OF NONCONFORMING QUADRILATERAL FINITE ELEMENT METHODS FOR NONLINEAR COUPLED SCHRODINGER-HELMHOLTZ EQUATIONS
《Journal of Computational Mathematics》2024年第4期979-998,共20页Dongyang Shi Houchao Zhang 
supported by the National Natural Science Foundation of China(Grant No.12071443);by the Key Scientific Research Projects of Henan Colleges and Universities(Grant No.20B110013).
The focus of this paper is on two novel linearized Crank-Nicolson schemes with nonconforming quadrilateral finite element methods(FEMs)for the nonlinear coupled Schrodinger-Helmholtz equations.Optimal L^(2) and H^(1) ...
关键词：Schrodinger-Helmholtz equations Nonconforming FEMs Linearized Crank-Nicolson scheme Optimal error estimates 
ONE-PARAMETER FINITE DIFFERENCE METHODS AND THEIR ACCELERATED SCHEMES FOR SPACE-FRACTIONAL SINE-GORDON EQUATIONS WITH DISTRIBUTED DELAY
《Journal of Computational Mathematics》2024年第3期705-734,共30页Tao Sun Chengjian Zhang Haiwei Sun 
supported by the NSFC(Grant No.11971010);the Science and Technology Development Fund of Macao(Grant No.0122/2020/A3);MYRG2020-00224-FST from University of Macao,China.
This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed delay.For 1D problems,...
关键词：Fractional sine-Gordon equation with distributed delay One-parameter finite difference methods Convergence analysis ADI scheme PCG method 
GENERALIZED JACOBI SPECTRAL GALERKIN METHOD FOR FRACTIONAL-ORDER VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH WEAKLY SINGULAR KERNELS
《Journal of Computational Mathematics》2024年第2期355-371,共17页Yanping Chen Zhenrong Chen Yunqing Huang 
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.41974133,12126325);by the Postgraduate Scientific Research Innovation Project of Hunan Province(Grant No.CX20200620).
For fractional Volterra integro-differential equations(FVIDEs)with weakly singular kernels,this paper proposes a generalized Jacobi spectral Galerkin method.The basis functions for the provided method are selected gen...
关键词：Generalized Jacobi spectral Galerkin method Fractional-order Volterra integ-ro-differential equations Weakly singular kernels Convergence analysis 
UNIFORM SUPERCONVERGENCE ANALYSIS OF A TWO-GRID MIXED FINITE ELEMENT METHOD FOR THE TIME-DEPENDENT BI-WAVE PROBLEM MODELING D-WAVE SUPERCONDUCTORS
《Journal of Computational Mathematics》2024年第2期415-431,共17页Yanmi Wu Dongyang Shi 
supported by the National Natural Science Foundation of China(Grant Nos.12201640,12071443).
In this paper,a two-grid mixed finite element method(MFEM)of implicit Backward Euler(BE)formula is presented for the fourth order time-dependent singularly perturbed Bi-wave problem for d-wave superconductors by the n...
关键词：Time-dependent Bi-wave problem Two-grid mixed finite element method Uniform superclose and superconvergent estimates 
A SCALAR AUXILIARY VARIABLE (SAV) FINITE ELEMENT NUMERICAL SCHEME FOR THE CAHN-HILLIARD-HELE-SHAW SYSTEM WITH DYNAMIC BOUNDARY CONDITIONS
《Journal of Computational Mathematics》2024年第2期544-569,共26页Changhui Yao Fengdan Zhang Cheng Wang 
supported by NSFC(Grant No.11871441);supported by NSF(Grant No.DMS-2012669).
In this paper,we consider the Cahn-Hilliard-Hele-Shaw(CHHS)system with the dynamic boundary conditions,in which both the bulk and surface energy parts play important roles.The scalar auxiliary variable approach is int...
关键词：Cahn-Hilliard-Hele-Shaw system Dynamic boundary conditions Bulk energy and surface energy Scalar auxiliary variable formulation Energy stability Convergence analysis 
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 DEEP LEARNING BASED DISCONTINUOUS GALERKIN METHOD FOR HYPERBOLIC EQUATIONS WITH DISCONTINUOUS SOLUTIONS AND RANDOM UNCERTAINTIES
《Journal of Computational Mathematics》2023年第6期1281-1304,共24页Jingrun Chen Shi Jin Liyao Lyu 
supported by National Key R&D Program of China under grants 2018YFA0701700,2018YFA0701701,and NSFC grant 11971021;supported by the Natural Science Foundation of China under grant 12031013.
We propose a deep learning based discontinuous Galerkin method(D2GM)to solve hyperbolic equations with discontinuous solutions and random uncertainties.The main computational challenges for such problems include disco...
关键词：Discontinuous Galerkin method Loss function Convergence analysis Deep learning Hyperbolic equation 
EXPONENTIAL TIME DIFFERENCING-PADE FINITE ELEMENT METHOD FOR NONLINEAR CONVECTION-DIFFUSION-REACTION EQUATIONS WITH TIME CONSTANT DELAY
《Journal of Computational Mathematics》2023年第3期370-394,共25页Haishen Dai Qiumei Huang Cheng Wang 
NSFC 11971047(Q.Huang)and NSF DMS-2012669(C.Wang).
In this paper,ETD3-Padéand ETD4-PadéGalerkin finite element methods are proposed and analyzed for nonlinear delayed convection-diffusion-reaction equations with Dirichlet boundary conditions.An ETD-based RK is used ...
关键词：Nonlinear delayed convection diffusion reaction equations ETD-Pad´e scheme Lipshitz continuity L^(2)stability analysis Convergence analysis and error estimate 
A VARIATIONAL ANALYSIS FOR THE MOVING FINITE ELEMENT METHOD FOR GRADIENTFLOWS
《Journal of Computational Mathematics》2023年第2期191-210,共20页Xianmin Xu 
supported in part by NSFC grants DMS-11971469;the National Key R&D Program of China under Grant 2018YFB0704304 and Grant 2018YFB0704300.
By using the Onsager principle as an approximation tool,we give a novel derivation for the moving finite element method for gradient flow equations.We show that the discretized problem has the same energy dissipation ...
关键词：Moving finite element method Convergence analysis Onsager principle 
SUPERCONVERGENCE ANALYSIS OF A BDF-GALERKIN FEM FOR THE NONLINEAR KLEIN-GORDON-SCHRODINGER EQUATIONS WITH DAMPING MECHANISM
《Journal of Computational Mathematics》2023年第2期224-245,共22页Dongyang Shi Houchao Zhang 
supported by the National Natural Science Foundation of China(No.11671369,No.12071443);Key Scientific Research Project of Colleges and Universities in Henan Province(No.20B110013).
The focus of this paper is on a linearized backward differential formula(BDF)scheme with Galerkin FEM for the nonlinear Klein-Gordon-Schrödinger equations(KGSEs)with damping mechanism.Optimal error estimates and super...
关键词：KGSEs with damping mechanism Linearized BDF Galerkin FEM Optimal error estimates SUPERCONVERGENCE 
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