Search
Search Results
-
Crank–Nicolson Schemes for Sub-Diffusion Equations with Nonsingular and Singular Source Terms in Time
In this work, two Crank–Nicolson schemes without corrections are developed for sub-diffusion equations. First, we propose a Crank–Nicolson scheme...
-
An extrapolated Crank-Nicolson virtual element scheme for the nematic liquid crystal flows
In this paper, we consider the numerical approximations of the Ericksen-Leslie system for nematic liquid crystal flows, which can be used to describe...
-
An Implicitly Extended Crank–Nicolson Scheme for the Heat Equation on a Time-Dependent Domain
We consider a time-step** scheme of Crank–Nicolson type for the heat equation on a moving domain in Eulerian coordinates. As the spatial domain...
-
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...
-
A Fully-Decoupled Artificial Compressible Crank–Nicolson–Leapfrog Time Step** Scheme for the Phase Field Model of Two-Phase Incompressible Flows
In this paper, we consider efficient numerical approximations for the phase field model of two-phase incompressible flows. To develop...
-
-
Optimized Ventcel-Schwarz methods for the Cahn-Hilliard equation discretized by the stabilized linear Crank-Nicolson scheme
The stabilized linear Crank-Nicolson (SL-CN) scheme is a very important time discretization for the Cahn-Hilliard (CH) equation since it is an...
-
Crank-Nicolson Finite Difference Scheme for Time-Space Fractional Diffusion Equation
This paper aims in develo** the Crank-Nicolson type of finite difference scheme for space-time fractional order diffusion equation (TSFDE) with a...
-
Existence of smooth solutions to the 3D Navier–Stokes equations based on numerical solutions by the Crank–Nicolson finite element method
A Crank–Nicolson finite element method is proposed to solve the time-dependent Navier–Stokes equations. We prove that for a given smooth initial...
-
Unconditionally optimal error estimate of the Crank–Nicolson extrapolation Galerkin finite element method for Kuramoto–Tsuzuki equation
In this paper, a linearized Crank–Nicolson extrapolation Galerkin finite element is investigated for two-dimensional Kuramoto–Tsuzuki equation and...
-
Optimal Error Estimates of SAV Crank–Nicolson Finite Element Method for the Coupled Nonlinear Schrödinger Equation
In this paper, we reformulate the coupled nonlinear Schrödinger (CNLS) equation by using the scalar auxiliary variable (SAV) approach and solve the...
-
Strong-Norm Convergence of the Errors of the Projective-Difference Method with the Crank–Nicolson Scheme in Time for a Parabolic Equation with a Periodic Condition on the Solution
AbstractIn a separable Hilbert space, a smoothly solvable linear variational parabolic equation with a periodic condition on the solution is solved...
-
BDF2 and Crank–Nicolson schemes
In this chapter, we discuss two time-step** techniques that deliver second-order accuracy in time and, like the implicit Euler method, are...
-
A Single-Step Correction Scheme of Crank–Nicolson Convolution Quadrature for the Subdiffusion Equation
We develop a new correction scheme for time discretization of the subdiffusion equation based on the fractional Crank–Nicolson convolution...
-
A Modular Voigt Regularization of the Crank-Nicolson Finite Element Method for the Navier-Stokes Equations
We study a modular Crank-Nicolson based Voigt regularization algorithm for the Navier-Stokes equations. This algorithm adds a minimally intrusive...
-
The Crank-Nicolson Type Compact Difference Schemes for a Loaded Time-Fractional Hallaire Equation
In this paper, we study a loaded modified diffusion equation (the Hallaire equation with the fractional derivative with respect to time). The compact...
-
The Completely Discretized Problem of the Dual Mixed Formulation for the Heat Diffusion Equation in a Polygonal Domain by the Crank-Nicolson Scheme in Time
The purpose of this paper is to prove a priori error estimates for the completely discretized problem of the dual mixed formulation for the heat...
-
A Crank–Nicolson-type finite-difference scheme and its algorithm implementation for a nonlinear partial integro-differential equation arising from viscoelasticity
A Crank–Nicolson-type finite-difference scheme is proposed and analyzed for a nonlinear partial integro-differential equation arising from...
-
An efficient data assimilation based unconditionally stable scheme for Cahn–Hilliard equation
This paper aims to present an efficient numerical method for solving the Cahn–Hilliard equation incorporating a data assimilation term. The data...
-
A New Analysis for a Super-Convergence Result in the Divergence Norm for Lowest Order Raviart–Thomas Mixed Finite Elements Combined with the Crank–Nicolson Method Applied to One Dimensional Parabolic Equations
We consider the \({\mathrm{I \! R}}{\mathbb T}_0\)...