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Unconditional superconvergence analysis of an energy dissipation property preserving nonconforming FEM for nonlinear BBMB equation
In this article, an energy dissipation property preserving modified Crank–Nicolson (CN) fully-discrete scheme is developed and investigated with the...
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Unconditional superconvergence analysis of an energy-stable finite element scheme for nonlinear Benjamin–Bona–Mahony–Burgers equation
In this paper, an energy-stable Crank–Nicolson fully discrete finite element scheme is proposed for the Benjamin–Bona–Mahony–Burgers equation....
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Unconditional superconvergence analysis of a structure-preserving finite element method for the Poisson-Nernst-Planck equations
In this paper, a linearized structure-preserving Galerkin finite element method is investigated for Poisson-Nernst-Planck (PNP) equations. By making...
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Unconditionally Superconvergence Error Analysis of an Energy-Stable and Linearized Galerkin Finite Element Method for Nonlinear Wave Equations
In this paper, a linearized energy-stable scalar auxiliary variable (SAV) Galerkin scheme is investigated for a two-dimensional nonlinear wave...
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Convergence and superconvergence analysis of finite element methods for nonlinear Ginzburg–Landau equation with Caputo derivative
In this paper, we study and analyze the time fractional Ginzburg–Landau equation (FGLE) using finite element methods (FEMs) in space and L 1 scheme in...
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Convergence and Superconvergence Analysis of a Nonconforming Finite Element Variable-Time-Step BDF2 Implicit Scheme for Linear Reaction-Diffusion Equations
In this paper, an effective fully-discrete implicit scheme for solving linear reaction-diffusion equations is constructed by using the...
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Second-order energy-stable scheme and superconvergence for the finite difference method on non-uniform grids for the viscous Cahn–Hilliard equation
In this work, we construct a fully discrete scheme with finite difference method based on the staggered grids for the viscous Cahn–Hilliard equation....
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Superconvergence analysis of a BDF-3 finite element method for nonlinear parabolic equation
Superconvergent property for a nonlinear parabolic equation with 3-step backward differential formula (BDF) Galerkin finite element method (FEM) is...
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Unconditionally superconvergent error estimates of a linearized Galerkin finite element method for the nonlinear thermistor problem
In this paper, a linearized Galerkin fully-discrete scheme is proposed and investigated for the time-dependent nonlinear thermistor problem, where...
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Unconditionally convergent and superconvergent FEMs for nonlinear coupled time-fractional prey–predator problem
In this paper, a linearized L 1-Galerkin finite element method (FEM) is proposed to solve the nonlinear coupled time-fractional prey–predator problem....
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Superconvergence Error Estimate of a Finite Element Method on Nonuniform Time Meshes for Reaction–Subdiffusion Equations
In this paper, we consider superconvergence error estimates of finite element method approximation of Caputo’s time fractional reaction–subdiffusion...
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Unconditional Optimal Error Estimates of Linearized, Decoupled and Conservative Galerkin FEMs for the Klein–Gordon–Schrödinger Equation
This paper is concerned with unconditionally optimal error estimates of linearized leap-frog Galerkin finite element methods (FEMs) to numerically...
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Error estimates for the finite element method of the chemotaxis-Navier–Stokes equations
In this paper, we present a se-implicit backward Euler finite element scheme for the chemotaxis-Navier–Stokes equations. By introducing some sharp...
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Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations
In this paper, we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations. Optimal error...
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Maximum-Norm Error Estimates of Fourth-Order Compact and ADI Compact Finite Difference Methods for Nonlinear Coupled Bacterial Systems
In this paper, by introducing two temporal derivative-dependent auxiliary variables, a linearized and decoupled fourth-order compact finite...
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Unconditionally optimal error estimates of a linearized weak Galerkin finite element method for semilinear parabolic equations
In this paper, we consider the unconditionally optimal error estimates of the linearized backward Euler scheme with the weak Galerkin finite element...
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Optimal Error Analysis of Linearized Crank-Nicolson Finite Element Scheme for the Time-Dependent Penetrative Convection Problem
This paper focuses on the optimal error analysis of a linearized Crank-Nicolson finite element scheme for the time-dependent penetrative convection...